ABS is more soluble in solvents than is PLA. Acetone will dissolve it, which can be a benefit because it allows vapor smoothing, but can be a problem with some paints which have solvents other than water. Try out any new paint on a scrap piece. Apply a thick dot of the paint, let it sit for a couple of minutes, and then wipe it off. If there is a change in the shape or color where the dot had been, the paint may be dissolving the ABS.
Acrylic has a water base and does not attack ABS.
A paint that attacks ABS may be fine, but there may be some color bleeding of the ABS color into the paint. A translucent (or clear) ABS would minimize the problem, since does not contain any pigment.
Spray painting may work better because the paint is undisturbed once applied. Brushing on paint will mix the dissolved layer with the unaltered paint.