Depending on the look and feel you want there are any number of paints that I've used that lasted through many washings - some of them were not originally intended to have been on the fabric in question - thank you DGS (who was not so dear for awhile after that little episode of getting into his mom's paints!) The ones he got into were the little bottles of acrylic paint from Walmart that she was using to paint on flower pots. I think the brand is Apple Barrel.
The smaller sized ones that have a little dropper type end that leave a raised line like cake decorating will crack and peel after a time when used on t-shirts or sweatshirts and put in the dryer.
I have also very successfully used Crayola crayons colored very intensely on muslin and ironed (on cotton setting) between two sheets of waxed paper. If you do not color intensely or if you use 'off brand' crayons it will fade out, but otherwise it will last a long time. I did it on a quilt that lasted 15 - 20 years before the vintage muslin part that was not colored wore out.