Can Poly1305-AES be used with AES-256?
Yes, Poly1305-AES can safely be modified to use AES-256 rather than AES-128; but if AES is implemented in software beware of not introducing a timing vulnerability in the implementation.

Change of the cipher in Poly1305-AES is explicitly endorsed; quoting D. J. Bernstein's The Poly1305-AES message-authentication code


  There is nothing special about AES here. One can replace AES with an
  arbitrary keyed function from an arbitrary set of nonces to 16-byte strings. (..)
  Perhaps AES will be broken someday. If that happens, users should switch to Poly1305-AnotherFunction. Poly1305-AnotherFunction provides the same security guarantee relative to the security of AnotherFunction.


The reference implementation of Poly1305-AES in software has AES carefully optimized to reduce cache-induced timing dependencies; beware that whatever AES-256 implementation is used is at least as good from this standpoint. If AES is implemented using AES-NI, in hardware, or otherwise in constant time (e.g. on a CPU without cache), that's a non-issue.

More generally, in any system using AES-128, if we can double the key size, we can safely use AES-256 instead from a theoretical standpoint; and if we can tolerate the slightly slower operation, and do not introduce a vulnerability (in particular by timing of cache misses), that's fine from a practical standpoint.