Michigan and Harvard have a full one-year for reseach build into the 4 year residency.
The thing is, if during or at the end of your residency, you decide to spend an extra full-year just doing research -- I bet it would be easy at many academic programs to find funding. You can probably also do a "fellowship" -- which has funding and involves lots of research, but also has the added benefit of giving you something extra on your resume (i.e. I did a fellowship in so and so).