It won't be fresh juice, but Tropicana has a tangerine blend in their not-from-concentrate cartons. If nothing else, it might help you figure out what taste notes to bring out, if you decide you don't want to use that.
My experience with tangerines are that they are both sweeter and tarter than standard juice oranges. A little lemon juice, a bit of sugar or honey and some grated orange peel will probably give you a good flavor.
Besides, you're teaming it with Chipotle. In the words of Peter Schikele on P.D.Q. Bach's concerto for Bagpipe and Lute, "It's a nice lute. Think about the lute while you listen to the bagpipe."
But seriously: if you can't find a tangerine in your local market, add a little peel from your oranges. Chipotle works well with sweet, so a little extra sugar won't hurt either.