Generally people pick their support based on their own team comp or the enemy team comp. This is fine, but since supports are usually fight against each other in small fights I think it's also important to counter pick against the opponent support when given the opportunity.

Here I will share my own support counter pick guide for most of the mainstream support heroes based on my own experiences as well as what I've noticed in competitive play/high elo play. Keep in mind that counter picking the support position is slightly different than counter picking the DS lane, since you aren't laning against each other you'll almost never be able to completely hard counter the enemy support. However, you can easily secure a 60/40 or even a 70/30 advantage which will make your game much easier. This is also why it's important to have a wide range of heroes at your disposal when playing support, it gives you and your team a huge edge over the opponents.

Zip

Counter picks: Grakk, Ata

I usually ban Zip just to save myself a few years, but if your team didn't ban him then Grakk IMO is a great pick against him given that you could hit your hooks. A godly Zip can use his S2 to block your hooks, but you probably won't see that since you're hard stuck in Diamond (jk). The main idea is for Grakk to hook one of the enemies and focus fire him before Zip could save him. Ata is another good choice as well since Zip is relative weak early game, you can invade the shit out of his jungle in the early game without dying. In team fights, you can slam down your ult to prevent Zip from sucking his team and rolling away.

Grakk

Counter picks: Chaugnar, Roxie, Thane, Mina, Wonder Woman.

No explanation needed for Chaugnar, you can block his hook with your S1. If you or a teammate gets hooked you can just ult. Roxie/Thane/Mina are all relatively tanky and can counter engage if they get hooked. You generally want to pick heroes that can counter engage, and you generally want to avoid squishy heroes because you most likely will just get focused down if Grakk lands the hook.

Chaugnar

Counter picks: Annette, Arum, Aleister

Chaugnar is annoying AF because he can just stack his S2 on a bird, S1, ult, and just tower dive the shit out of your MM with Disrupt. My favorite hero to go up against Chaug is Annette, because she can just ult and literally block the enemy Chaugnar from getting close to your MM. Otherwise Arum/Aleister ult works as well, as usual.

Arum

Counter picks: Zip, Gildur, Sephera

Zip can save his team from Arum ult with his S2, Gildur and Sephera can poke the shit out of her. Arum isn't necessarily a strong hero right now, but she's definitely annoying. She's strong against melee range heroes, but weak against poke heroes.

Y'Beneth

Counter picks: Arum, Baldum

A good Y'Beneth is one of the most annoying heroes in the game. He's tanky AF and has a ton of regen with his ult so he's not afraid of poke, he also has a butt load of CC and in general is just very annoying. One of the ways I like to deal with him personally is to watch him with Arum/Baldum, which basically cancels Y'Beneth's ult. Aleister ult works as well, but he's too squishy and his ult can be interupted.

Annette

Counter picks: Riktor, Gildur, Sephera

Annette is really good at counter-engaging, so you don't want to pick a dive heavy hero against her. Instead you want to pick heroes that can straight up bully her like Riktor, or heroes that can poke her out like Gildur/Sephera.

Gildur

Counter picks: Chaugnar, Veres, Peura

Chaugnar is self explanatory, literally nothing Gildur can do when you have your ult. Veres is absolutely amazing against Gildur since she has CC immune, and can just straight up bully him early/mid game. Peura is pretty good against strong poke comps like Gildur/Elsu combos, since she can just heal right back up without having to go back to fountain.

Krizzix

Counter picks: Wonder Woman, Y'Beneth

If you see an enemy Krizzix, just lock down Wonder Woman and the match is won 80% of the time. You literally just bully the little froggo all game, and there's nothing he can do to you. If you get caught off guard with a flicker S2, just counter engage with your ult. Same idea with Y'Beneth, you see Krizzix charging in with S2 just ult.

Wonder Woman

Counter picks: Maloch, Y'Beneth, Mina

Nothing WW can do against Maloch, he's too tanky for her and he does true damage with his S1. You literally just chase her around with your S1 from start to end. Y'Beneth is another good counter pick IMO, she doesn't have enough damage to threaten you and she can't stop your ult. Most importantly, the enemy MM is generally positioned behind WW in a fight in order to receive the shield from her ult, that's when it makes it easy for you to go in, clap both with them with your S2 and ult. Same idea with Mina, the fact that the enemies will stand close to their WW makes it easy for you to hit multiple people with your S2 & ult. If they don't stand together, then WW is ulting the air so it's win win either way.

Mina

Counter picks: Chaugnar, Roxie, Marja

Again Chaugnar is self explanatory against CC heavy heroes. I've done well against Mina with Roxie, because I can purify all of her CC with a support item, but there's nothing she can do against my ult unless she takes purify over flicker. Marja support is another option to consider, since you can just keep poking/stacking your passive from a distance and there's nothing Mina can do to you especially when you still have your ult.

Omega

Counter picks: Wonder Woman

Wonder Woman's skill set is really good against Omega IMO. She's not afraid of him in a fight, and if he ults in to push your team around you can counter engage with your own ult.

Veres

Counter picks: The user

A good Veres support is the most annoying thing, lucky for you guys nobody plays Veres support in Diamond (jk not rly). Nothing really stands out as a counter pick, I'm not a huge fan of Florentino support unless you're just running circles around your opponent. In a match where the opponents have equal skill Flor support is pretty gimmicky. I hate playing against Omega when I'm playing Veres because he just pushes me around and messes up my combos, but I'm not the greatest Veres player so it might just be a me thing.

Riktor

Counter Picks: Omarr, Veres, Maloch

You generally want to pick heroes that can fight Riktor early game, as well as heroes that poses a threat to the enemy backline since Riktor is very offensive and not very good at protecting the ADC. You generally want to avoid squishy supports since you'd end up getting forced out of bushes and end up with no vision.

Omarr

Counter picks: Omega

Omega hard counters him IMO, Omarr needs to hit enemies with his ult in order to regain health and Omega can literally just ult and push him away. The bigger Beyblade wins.

Cresht (Post buff)

Counter picks: Annette, Maloch

Cresht is getting a huge buff tomorrow that removes the rage requirement for his ult, this means he can use his ult much more consistently and he becomes one of the top supports since he can just dive in with ult & disrupt. When going up against Cresht, you want to take disrupt yourself as well and pick heroes that can counter-engage like Annette. Maloch is another good choice as well since he can both engage & counter engage with his ult, and he does true damage which bypasses Cresht's huge shield.

Maloch (Post buff)

Counter picks: Superman

Maloch is extremely strong with his upcoming buff that grants him true damage as soon as he hits his S2. In the games I've played the counter pick I had the most success with is Superman. What you want to do is wait for Maloch to engage with his ult, and that's when you come in with your own Superman ult to push his team back. This makes it so that Maloch is separated from his team, and your team can just focus fire him when he jumps in.

Superman

Counter picks: Y'Beneth, Ata

When you see a Superman pick, you won't go wrong locking down Y'Beneth who can stop Superman's flight mode with all 3 of his skills. Ata is a good pick against him as well since he can stop Superman's flight mode with S1 & S2, and his ultimate locks Superman down unless he takes flicker.

Rouie

Counter picks: Superman, Omega, Annette, Grakk, Thane

Basically any hero that can push her and and drag her team out of her S2.

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That's all that comes to mind for now, there are a lot of heroes that I didn't include on this list because you don't really need to counter pick against them. Baldum is a good example for this, you don't really need to counter pick against him because pretty much every support hero can fight him well. At that point you're better off picking based on your own team comp as well as the enemy team comp.

If anyone wants to add to this, or want to know how to fight against a specific hero (whether it's counter picking or just the overall strategy) let me know in the comments and I'll try to get back.