I do my shirt designs upside down. To avoid conflict between the narrow neckline and the hoop/machine connection, I flip my design on the embroidery machine screen upside down and then I do the design by putting the hoop in at the shirt waist. I'm assuming the onesies can open wide on the bottom, so if you can flip your design upside down on your embroidery machine, you can do it that way.
There is a soft stabilizer on the market that I hear is very baby-skin friendly, but I can't remember what it's called; it should be available (and advertised as such) wherever a wide variety of ME stabilizers are sold.