According to the CIA World Factbook, the ethnicities of Guyana are:
East Indian 43.5%, black (African) 30.2%, mixed 16.7%, Amerindian 9.1%, other 0.5% (includes Portuguese, Chinese, white) (2002 estimate.).
Guyana is the only English-speaking country in South America and shares cultural and historical bonds with the Anglophone Caribbean. Guyana's two largest ethnic groups are the Afro-Guyanese (descendants of African slaves) and the Indo-Guyanese (descendants of Indian indentured laborers), which together comprise about three quarters of Guyana's population.
You can always go with "other" and write in Guyanese. If you identify as Afro-Guyanese and are descended from African slaves then you might identify as Black which is a choice (African-American/Black). If you are of East Indian descent then you might list Asian... and if you are both you can do that (list both) too.