I am, and there is a type called "black coffee." But maybe this sentence could mean 2 things:
- He likes his coffee when it is black.
- He likes his coffee black style.
I thought this might help you understand the sentence better. Sometimes you can talk like this in English. This is correct grammar and correct format.
Hope this helps!
"He likes his coffee black" is expressing a personal, consistent preference, a bit like saying "He likes his tea with sugar". "He likes his black coffee" would be used to express a present state, but not necessarily an ongoing preference: "In this moment, in this beautiful cafe, he likes his black coffee".