How to add cooldowns in a way that nobody will hate

Some people hate cooldowns. Myself included.
I'd hate for a cool skill gem to drop and than see it can only be used once every 30 seconds.

Other people like them for some reason.
Here is a way we can add them so everybody wins

Cooldown Maker Support gem
The skill that this is linked to has
x% increased damage, y% increased size
it however gains a z second cooldown.
You may only have W total cooldown gems on
(this is to prevent extreme burst in pvp)

I believe that this is a do able idea.

Eventually, as the game progresses we might be able to see more and more complex skill gems with more complex abilities.

Support. Though I believe this is something the Dev team has already considered.

I like this idea. The skill system seems to be about choice and this would certainly fit that.

This would definitely prevent a spam of the same skill. I like cooldowns and dislike them at the same time. Yes, they limit what you can do, but that means you have to use the skills more wisely and actually requires thinking, instead of spamming the same skill over and over. I do believe the basic attack is what you should use if you just want to faceroll through the game.

Cooldowns balance the game. They allow you to have a really powerful skill that doesn't break the game!

I'm usually against cooldowns myself, but I actually really like this idea.

I'm not a big fan of cooldowns for the very reason that the cooldowns are used to limit a skill that is too powerful otherwise. Rarely does this change the fact that the skill is too powerful. Just makes everyone feel better about it being there. I like your idea to have a control in place to further limit their use.
To me, if you are going to have a cooldown skill, it should be like a Hail Mary. It is effective but something that you can rarely ever do. Perhaps a good way to work cooldowns is to provide a global cooldown timer. This would allow the possibility for multiple cooldown skills but remove the possibility for chaining them.