Amari has recently been popular for both boys and girls in the African-American community. There are several names ending in -mari that have become popular for African-American boys recently; Amari is one of the few that is also frequently found for girls.
Omari is a Swahili version of Omar
. I haven't been able to find confirmation, but Amari might be a Swahili version of Ammar, an Arabic name meaning "long-lived". Or it could just be a recent creation based on Omari. More research is needed to make sure.