What about silk-screening?
In a merchandising workshop I have worked with it on cloth, paper, mugs and glasses, and its also used to print on lighters and pens, that's plastic and small enougth to be compared to LEGO pieces. It's not very expensive, but requires some knowledge, practice
(difficulty increases with the numbers of colors you want to print together in the same design piece), workspace, and tolerance to the chemicals necessaries to prepare the inks and to clean the utensils.
It never occured to me to try to print on a LEGO piece when I had the chance working there, the idea just gives me an impulse to do so, but I don’t have the equipment nor the space, and neither the time (for now)!