What's the generic word for weekly/monthly etc. service?
There are several possible words that could be used here:
- regular, as @Lawrence suggests
- periodic (Oxford, definition 1, "Appearing or occurring at intervals.")
- recurring or recurrent, which you used in your question.
- repeating is a perfectly valid word for this use.
It's a regular service.
regular adjective 2 Recurring at uniform intervals. ‘a regular monthly check’ - ODO