I'm thinking of denying my co-worker's request to take every Monday off all summer long
Is that true? Why do you want to deny your co-workers request?
I'm busy on Mondays and I can't do it
If you and your co-worker are having scheduling issues on Mondays, you should compromise. Compromising will enable the both of you to benefit from having monday off, by alternating Mondays, for example.
That's too much trouble
It's important that you compromise with your coworker's so that in the future they will do favors for you.