I finally figured out how to embroider onesies on my embroidery machine!
Things that I learned:
1) Use a sticky stabilizer - otherwise the fabric tends to bunch and shift
2) Use a water soluble stabilizer on top of the fabric to keep the threads from sinking into the onesie
3) Hoop the onesie and then flip it inside out to keep the back out of the way
4) The back is pretty rough after being stitched so it probably needs some kind of backing on it - I still have to figure out what kind of product I want to use for that
In general I am pretty pleased with the final product!