Are all alliums out? IE, no onion either?
Are you going for more of a Caribbean vibe or central American vibe?
For more of a Mexican-ish flavor I usually use some combo of epazote or oregano, bay, cumin, and maybe a chipotle in Adobe or two or fresh peppers like serrano or jalapeno...and salt. I think you can just leave out the allium and still get good results. You could also add some bacon or a ham hock or something.