You're talking about wood stain? Probably not.

If the paint is flat, it's going to be very porous and will absorb and hold the stain. I assume this is what you have, since you would have probably been able to wipe it off of enamel paint pretty well.

Stains come in two types: dye and pigment. Dyes are dissolved in a solvent, pigments are fine powders that have to be suspended in a liquid to do their job. If it's a pigment type, and porous paint, you'll likely never get those tiny particles out of the paint. If it's a dye type, you could try using whatever solvent (paint thinner or water) on a rag and see if it takes it out. This is a totally wild guess, so take it with a grain of salt.

Failing that, you'd have to repaint. Might have to use a stain blocker primer like Kilz to keep it from bleeding through.

Ahh, No.

Thanks everyone... we just painted over it and it looks okay...