Oats are a good crop that is sometimes used to shade out weeds. I would not plant rye with oats for this reason. I would plant my oats for spring, utilize them until fall, then overseed in the fall with the rye. Not saying it wouldnt work, but to best utilize the protein of your oats I would just wait on the rye.

TexasAggieBowhunter
Certified Professional Agronomist