Which full-length black musical comedy challenged the old custom of white actors' "blacking up," was written and performed by african americans (some in white face), and employed the emerging ragtime musical syncopations of early black revues?

Bob Cole's A Trip to Coontown (1898)

Explanation:

Robert Allen Cole was an African American author, dramatist, on-screen character, chief and stage maker.  

In a joint effort with Billy Johnson, he composed and delivered A Trip to Coontown (1898), the primary melodic completely made and possessed by dark entertainers. The well known melody La Hoola Boola (1898) was likewise a consequence of their coordinated effort.  

Cole later banded together with siblings J. Rosamond Johnson, piano player and vocalist, and James Weldon Johnson, musician, guitarist and legal counselor, which came about in more than 200 melodies.