None of the paints you're going to use to paint your home is "safe" for a cat (or a human) to ingest, so if that is the concern, then we're really only talking about keeping the cat out of the area while drying. Paint dry times vary a bit, but latex is usually 2-3 hours and oil-based is usually around 6-7 hours. Once dry I think you can let the cat near it.
However, I don't really think that's totally necessary. We've had 3 cats for many years and have painted all over the house with none of the cats getting into trouble with it after it's been applied. While cats are curious, they don't just eat everything they come across, they're more likely to get it on their paws and track it around than anything else and so we only kept them out during the active painting time.