Sounds like a crime against humanity.

Getting paint to stick to marble could be nasty. Can you build a structure over it then paint that?

I am also curious why you would want to paint over marble. It is a beautiful material. But of course it's possible that after time it doesn't look so good anymore or its colour clashes with the rest of its surroundings.

Painting marble isn't that difficult. But I must say I'm unfamiliar with North American paint products so I have to speak generally. I think there are two roads to choose.

First, you could use an oil based primer and paint. Use a primer that's meant for flat surfaces like metal or plastic, as opposed to a primer that's meant for a rough surface like wood. The difference between the two types of primers lies in the adhesion process. A wood primer sticks by permeating the surface, filling in all the pores and crevaces in the wood. A metal/plastic primer just lays down a thin but very sticky layer on which other paints can adhere.

A slight sanding of the marble could help, use 80 or 120 grit to roughen it up a little. But it's not by definition necessary. Sanding will destroy the marble's look for good. In case you might want to preserve the marble for when you later change your mind and want to get rid of the paint, it's still possible if you haven't sanded it. The primer will still make sure you get good adhesion. Just make sure the surface is super clean before applying the primer.

The second option is using a special tile paint. There are two part tile paints available (at least here in Europe) to paint over your shower or kitchen. I guess it will work on marble as well, though I haven't had any experience myself using this on marble. With this paint it is necessary to roughen the surface up with a very rough grit, like 24 or 36, so there's no more possibilty restoring the marble later on. Because it's a two part paint where drying relies on a chemical reaction inside the paint instead of the solvent evaporating out of it, it becomes very hard and scratch resistant. Future removal without harming the surface beneath is close to impossible.
  

You could physically sand it to rough it up, but you could also use an etching solution on it first. Etching is a mild acid. You usually pick it up in powdered form, mix it with warm water and scrub it with a wire brush. Again this is going to white out and destroy the look of the marble but it would give a nice surface once you rinse it to get paint to stick to. I agree though oil based primer if you go that route, or a two part Epoxy based paint. You could also look at a eleastromeric masonry and stucco paint, or a masonry waterproofer. I'm not going to tell you they would last forever, but they would be too difficult to work with and you should get quite a few years from them.