If they're cousins, then no, they don't have to use the suffixes, assuming they're around the same age. "-chan" is reserved for close friends/family, but if they're close, no suffixes are necessary. If one's older, then that's a different story--the younger one should use "-san," but, again, depends on the cousin being addressed. Again, if they're close, formality may not be an issue, so there could be room to bend the rules.

If they're aunt and niece, though, niece should probably be appending "-san" whenever she addresses the aunt, at the very least, or be calling her "obasan." The aunt can either use the niece's name (no suffixes) or address her as "-chan" as well.