What can I use for a mermaid government?

You mean just a society of mermaids? Just make everything the same as it is with humans, only they're mermaids and live in the ocean.

Or do you mean something else, like mermaids exist and run/participate in the government for everyone, including mermaids AND humans? That would be tougher, but from what cartoons and movies based on mermaids that I've seen, it looks like mermaids can breathe outside of water, so you'd have to make meetings and whatnot with humans out on a boat and the mermaids swimming up to the surface.