When looking for funding, keep in mind that the poster project is a multi-disciplinary project. You might think of it as a science, math, or language project but it involves research, language skills, editing, keyboarding, art, various aspects of the actual topic and community involvement. Many funders like a project that involves many areas of learning.
School Budget

Ha, ha. Well, this does happen but let us move on.
School Support Groups
Many schools have PTO's, parent networks, and local groups which try to support creative, non-budget projects for schools. The same groups that fund a field trip are likely to support a poster project.
Cultural Councils are also a good place to look. The art, writing, and community involvement makes this an attractive project for funding. Certain poster topics of local interest could also help.
Local Businesses
Yes, everybody hits on the pizza guy, particularly the sports teams. But, consider other businesses, particularly those with waiting areas for the customers. Your poster provides art, community support, and something for people to read if in a waiting area. Waiting areas are not just in medical offices but also in tire stores and repair shops, hair salons, dining establishments (including the pizza guy) and so on.
Since you proably have enough to do in the classroom (!), perhaps a parent volunteer could be the one to seek funding for the project. br>
Other Grants
There are many grant giving organizations and finding the right one can be difficult. For most non-local grant givers the cost of this project is less than many will fund. You might be able to attract one of these grant givers by considering a greater focus. Bring in other grades and schools in the system for an overall district project.