I found a way using Ink Jet Fabric Transfers. Usually these are used for t-shirts and cotton-based fabrics, but if you print your design and heat it onto the diaper using the "Synthetic" setting on the iron, it works perfectly! (Note: It says in the instructions for the fabric transfers that only a "cotton" setting on the iron will work. That's wrong in this case, and do not try that because it will melt the waxy coating off of the diapers instantly. So be weary of heat!)
The transfer sheets are 6 sheets for $8 at Walmart, and it's a full printer page, so the smaller the design you wish to print, the more diapers one sheet could potentially cover! Just thought this was worth sharing.~ I was very pleased with my result, at least!