In this scenario, I agree with the "don't get a cat" suggestion. However...
Your dogs might surprise you. Find a shelter which allows you to bring your dogs to bond with the other animals in a controlled and quiet space - like a separate room. First let your dogs get calm and comfortable with the new room. Then bring in a cat you think you would like (hopefully one with a history with dogs) in a crate or carrier and let your dogs sniff it. If the dogs start becoming aggressive, then you KNOW it is a bad idea.
But, if the dogs want to add a new member to the pack, they will start going into their "let's play" routine. The problem is whether or not they play too rough for the cat. There is no point to bringing in a cat into an environment where it will always be scared.
If the dogs and cat are comfortable with each other, then bring the cat out of the crate to play with the dogs. If you like the dynamic they are showing at the shelter, then you just might be able to bring a new member into your family.
But if at anytime this does not look like a good idea, it is not a good idea. Your hope for a new cat will be dashed for the time being.
Well introduce the dogs to the cat and make sure that you keep them far enough away that the cat so they don't hurt the cat and let them get to know each other then hopefully they will get along. Best of luck to you.
LouisJolliet gave you a great idea! Only thing I would possibly do different is to introduce the Cat to one Dog at a time first. Dogs act different "one on one" than they do when in a "pack". If each Dog seems ok with the Cat( and you may have to try various Cats), then see how they do all together. If any of them Really goes for the Cat, it may not be a good idea. Hope it does work, Cats are cool!:-).