Pseudo random permutation for arbitrary size domains
Ciphers with Arbitrary Finite Domains by Black and Rogaway have some options like Prefix Ciphers, Generalized Feistel networks , Cycle walking etc. 

Also Format preserving encryption has traits that you are looking for , but NIST standardized ones are patented by Voltage Inc.

In general Feistel networks + Cycle walking would give a good option for any arbitrary length (even or odd) domains .

This question has much better answer 
Is there a length-preserving encryption scheme?