The Lord has blessed me with a full time job since 1989 as church library director. I have the luxury of being in a very large church that makes this possible. There is also one other full time staff member and a part-time staff member along with about 30 volunteers. Most people don't realize the amount of time and work that goes into maintaining a church library. The church library is or can be a vital part of the church ministry. I would encourage you to pursue the possibility of a part-time paid position.
Our church is medium-sized, I guess - 500-600 members. My friend and I run the library on a volunteer basis and we have a committee of 7 or 8 other people. How much time we spends varies rather wildly from week to week, depending on what is going on, if there are books to process, what new projects we're setting for ourselves...so some weeks it might only be a few hours and other weeks I might spend quite a bit more. I personally don't ever spend enough that I would consider it a "part-time position" but that is in part because we share the responsibility with so many other people (who, for the most part, help with covering shifts in the library on Sunday mornings, evenings and Wednesday evenings). If I did it all, it would probably qualify!
I'm curious, though, those who are paid for this position, how big are your churches?