Joe Burrows (2-13) and Steve Davis (1-41) sent back two batsman.
Another wicket brought James Green (34) to the crease.
Bradley Stoke neared their target, but Cooper and Jon Rivers were on hand to make sure the visitors reached the finishing line with three wickets and seven overs to spare, at the end of another close contest.
Methodists 125-8
Bradley Stoke 3rds 130-7
Daniel Shearn