Translation:The supermarket has a rather good deli.
I really think "The supermarket has quite a good charcuterie" should be accepted. It's a fairly commonly used word in English, at least in England anyway. I don't think it really needs to be translated (although deli would be the obvious translation I agree)
According to Wordreference charcuterie can translate to cooked/cold meats, which I think is close enough to merit reporting. I welcome any native speaker to tell me if I'm wrong though. Also note that cold cuts/deli meats as in a collection of meats (I think as in a dish?) is assiette de charcuterie.
The supermarket has rather a good deli is more natural English and should be accepted. Originally I wrote the suggested answer as a literal translation but changed it as it didn't sound right to me as an English speaker.