There are many ways to go about this, but having a week of special events that highlight the features of the library is a great library fundraising idea that will help you as well as the community that the library serves. If you have any local authors of note, it might be a good idea to try to contact them and solicit their help. Authors always like publicity, and having a well-known name attached to one or more of your events is one of the best fundraising ideas out there.
Many children's authors, for example, are more than happy to help with fundraising by coming in and doing reading sessions for the children, and when the kids come in, so do their parents. This would be a great time for you to have a bake sale, or perhaps have one of our chocolate bar fundraiser ideas available.
You could even turn it into an afternoon-long event, with lots of opportunities for both parents and kids to enjoy the library and remind themselves what a treasure it is in the community. Library fundraisers are unique in that they work best if the people come to you rather than the other way around. When people visit a library, then invariably come out feeling positive about the experience, and this is a great way to get people in a generous mood.
The more events and special open days you can schedule, the more opportunities people have to come in and see for themselves why they should help the library with a donation, and the more money the library ends up making.