The OP's post is interesting as financing our village library to re-open after closure was something I was heavily involved with in our "save our library" group to re-open it as a community hub.
We had loads of ideas, many of which were adopted and the library re-opened and has been self financing for several years now.
Vending machines for hot & cold drinks, snacks etc.
Full range of "secretarial" services such as photocopying (A3 and A4), colour and B&W plus printing (again up to A3 size, colour), scanning, photo printing, thermal binding, etc.
Renting out side room/office to local groups, clubs and societies and also local businesses as a meeting room.
Selling goods of local small businesses, such as locally written/printed books, gifts, as well as locally relevant items such as local walking/cycling maps, village local history books, etc., displaying artworks on the walls from local artists where the library gets a commission on any sales.
Acting as commission agents for a few local amenities such as selling tickets for the local town's theatre productions, selling tickets for local coach trips and sightseeing trips, etc.
Commission on sales of other local business products, such as balloon displays for parties etc, photos printed onto plates, photo blocks, photo calendars etc.
It had a small car park, so now sell "permits" to locals to park in it's car park as the village has little "unrestricted" parking so locals struggle, whereas library users, who will only be there an hour or two, have no problem parking on the roads outside (with 2 hour restriction).
It also had quite a large "plot" it was sat in that had previously just been grass, so we marked it out and now rent out small plots for locals to rent an allotment, which also means we don't have to pay for grass cutting costs anymore nor other maintenance as the plot holders now fence off themselves and prune trees/shrubs that are within their plot!
The profits from all those "incidental" activities is enough to cover the running/overhead costs of the library such as rent, utilities, telecoms, insurance, etc. Thankfully, the local council still provide the books and were happy to continue doing so as long as they don't have to contribute to the running/overhead costs.