As I'm sure you're aware, paint is a "film finish." Since your slab was originally detailed as a carport, you can't be positive of the prep work or construction methods used under the slab.
First, take a piece of sheet plastic...about 2 feet square...lay it on the slab and tape it down on all four sides around the perimeter. Leave it there for a few days. If any moisture/condensation show up between the poly and the slab, that tells me that you don't have an effective moisture barrier under the slab and moisture vapor is able to pass through the slab, from bottom to top. It's not a foolproof test, as you're only running the test for 2 days and not through all the seasonal climate changes your slabe experiences over the course of a year. Nonetheless, it's a good indicator.
If you were to paint WITH moisture coming through the slab, the migrating moisture could cause problems with the paint adhering to the slab, and that's a mess you don't want to have to deal with down the road.
You can stain the slab, but there are limitations with acid stains as well. Jay wrote about many of the problems...grease, dirt, burnished (worn smooth from use) concrete, etc...
Look into acid staining. There could be compatability problems with those as well, but IF you have a moisture problem and want to "color" the concrete, a stain would be preferable to paint.