Use "there isn't any" (or "there aren't any) in most cases. "There ain't no" is something you might never use. It's not part of my normal speech, for example. But if you are friends with people who use that style of speech, then feel free to use it with them.

"There ain't no"... is slang, it is a very informal phrase

Hi Mikhail, some of the answers here are incorrect. 'There ain't no' is not incorrect English nor is it slang. It is correct in a number of dialects of English, but not in standard English. 'There isn't any' is standard English.

There ain't no Us a double negative. It is used in common speaking, but grammatically actually wrong. There ain't no = there are not no ...