Asian American Theatre Revuew has put together a long list of links. Oxford Companion to African American Literature edited by William L. Andrews, et al. A twenty-page introduction serves as a history. Contemporary Black American Playwrights and Their Plays by Bernard Peterson. Britannica's Internet Guide has a section for African-American theater.
Chapters give history, names of playwrights, producers, etc.
Hispanic Firsts by Nicolas Kanelloss tells the story of Hispanic Theater in the United States from 1598 to 1996 in a twenty-page chapter. Women playwrights of Diversity by Jane Peterson and Suzanne Bennett has a long article about Latina playwrights and biographical sketches of many of them. Ethnic Theatre in the United States edited by Maxine Schwartz Seller has a chapter on Puerto Rican theater. Algonkuin Players Theatre Company Native American Authors is fine if you know the name of the playwright.