There is so much that a really good author, poet, storyteller or illustrator can bring to the reading and the library experience that it's well worth looking for ways to fund this. Here are some ideas for how to get authors and artists involved with your library service.

Get together with neighbouring authorities to book an author or an artist for several days, or 2 events in one day, saving costs and building partnerships! Then you can share the cost and you'll probably be able to negotiate a better deal by making a multiple booking
You might also be able to set up this kind of sharing with a school, or with a local arts centre which includes literature in its programme
Develop contacts with your regional arts council. They will be able to recommend local authors, including talented up-and-coming people, and help you make the right choice for your library sessions and activities. (And as they're local the travel expenses will be less!)
Keep in touch with publishers too – they too may be promoting new talent or putting together promotional tours, so there could be mutual benefit here. Publishers will also be able to recommend to you authors to suit the event you are planning – eg. who works well with a particular age group
Many library authorities find local sponsorship to fund these events – maybe the local building society or supermarket. Sometimes a restaurant or hotel will support an event by providing a meal or accommodation for the author/s – and several authorities partner with local bookshops, who then share the costs and often have really good contacts when you're booking your author.
Remember virtual meetings as well – a number of authors have their own, and often very good websites, where young people can talk with them via email. Get some ideas from author sites in the TRF Links section. Or there may be possibilities with video-conferencing – perhaps sharing in an author session hundreds of miles away!