Either, I think. If you have one large set of data - 'copious amount of data'; if you have more than one large set of data - 'copious amount of data' (if you're talking about the data as a whole) or 'copious amounts of data' (if you consider each amount of data to be discrete).
However, I wouldn't say 'copious amount(s)' in the first place. Instead, I'd drop 'amount(s)' since it's redundant - so, 'copious data' - or, more likely, use simple English: 'large amount(s) of data'.
