It isn't any closer for you than Manchester, but, there is an Asian Market in Lebanon called Yiping's. About 1/2 mile from Yiping's, across the CT River in VT, is Piecemeal Pies where you can get a traditional rabbit meat pie for your rabbit fix.
If you do happen to venture to the Upper Valley and Yiping's doesn't have what you need, I imagine either the Hanover or Lebanon CO-OP Food Stores would be able to order it for you. Their butcher is usually really good with special orders.
My co-worker is from Hong Kong and he special orders through both Yipings and The Co-Op fairly regularly.
http://coopfoodstore.coop/
Closer to home, I have heard that Heath's in Center Harbor is pretty good with special orders, too.