A Sunday school or parish lending shelf is about as small as a library gets: a few dozen children's books and study guides that families borrow between sessions. It does not need anything elaborate. It needs the one thing every lending shelf needs, a way to know who has what so the books come back.
The trick is to keep the system as small as the shelf.
Keep the rules to one line
A shelf this size needs a single rule, not a policy. Something like "borrow a book, bring it back next week, no fuss" is enough. No fines, no membership, no forms. The whole charm of a parish shelf is that it is informal, and the system should protect that, not bury it.
The only record that matters
The one record worth keeping is the loan: which book went out, with which family, this week. Everything else is optional. You do not need a full catalogue of a shelf you can see in one glance, but you do need to know where a book is when it is not on the shelf, or it quietly disappears.
For thirty books you could do this on a card. The moment it grows past what a card can hold, or more than one helper is involved, a simple shared tool keeps it from sliding into nobody's-job territory.
When the shelf is part of a bigger church library
Often the Sunday school shelf sits inside a wider church library. If so, run it within the same library rather than as a separate scheme. The children's books are just one part of the church's collection, catalogued the same way, and lending works identically. That keeps one place to look instead of two competing lists.
The approach for the whole church library applies here in miniature, so if you are also setting up the main collection, fold the Sunday school shelf into it.
Running it with Your Book Nest
Your Book Nest handles a Sunday school shelf as easily as a full library, because it scales down as well as up. Catalogue the children's books, lend a copy to a family with a due date, and take it back, all in the browser with nothing to install. They sit in the same library as the rest of the church's collection, catalogued and lent the same way.
It stays as informal as the shelf: no fines, no patron accounts, borrowers are simply names. It is free for up to 100 books, far more than a Sunday school shelf needs, and the home page is a live demo you can try with no sign-up.