some people I know (and love) sub bourbon for the rye. normally I would agree to anything bourbon... because bourbon.
that said™, imo a Vieux Carré is quite a bit better with rye in it (and shows more authenticity).
now, not all rye is created equal and there are so many to choose from. to make things less complicated, these two suggestions are inexpensive, available, and both quite different and delicious in this classic:
Rittenhouse 100
Sazerac (only 45%/vol. but...)