Why does it not accept Dewi Lingo has black coffee? Why is the 'a' needed?
No that would be "Coffi du Dewi lingo". This construction is only used for "To have".
"Dewi Lingo has black coffee" should be accepted. The Welsh language does not have articles like "a" and saying "Dewi Lingo has black coffee" is more natural.
Yes "Dewi lingo has black coffee", should be correct. And yes Welsh doesn't have separate a indefinite article, but the indefinite aspect is portrayed in the base noun, and therefore "a black coffee" is acceptable as well.