Any paint that is specifically marketed for use on fabric will work. Thinner paints give a softer feeling on the fabric. Thicker paints can feel a little scratchy. Fabric markers are the most convenient type of fabric paint and cannot usually be felt at all. Metallic fabric paints such as Lumiere give cool effects when painted onto hand dyed fabric (dry the fabric first). I've used
puffy paints to good effect on t-shirt designs, but they can be ruined by being machine-dried.
The main problem with fabric paints is that they tend to wear off from abrasion in the washer and dryer. Turning inside out to wash, and line drying instead of machine-drying, can help slow the wear, but those are inconvenient for children's clothing.
Thickened Procion MX dye can be applied like fabric paint, but is more permanent, because it does not wear off.
(Two of my pages that are relevant are
Fabric Paints: a different way to color fibers, and
Sodium alginate, Superclear, and other dye thickeners, which is part of my
FAQ.)
Paula