The "visitcyprus" website, which we found pretty accurate, gives the hours as:
Tuesday - Saturday: 09:00 - 16:00, Sunday: 11:00 - 16:00 Monday: closed
When we visited, the church was open on our arrival so there was no need to hunt out the custodian. I think this is generally true.
Get quick answers from Agios Nikolaos tis Stegis Church staff and past visitors.