Here's another tip that's a multiple win for you and your contacts. Ask your contacts to help support community events or work on charitable projects. For example, volunteering and working on a Habitat for Humanity house building project can be a great bonding experience at the same time providing significant value to the community.
There may be lots of opportunities to recruit people for fund-raising events or campaigns, but I'd recommend more active projects. Fund raising is important and great to be involved in, but if at least part of your motivation is to build relationships with people with whom you volunteer, the typical fund raising scenario where everyone gets an office or cubicle and makes calls to potential donors isn't all that conducive to relationship-building.
The best projects to recruit for when you're also working on relationship building are short term projects that require physical effort - that's why a Habitat for Humanity project is so good. Particularly if your efforts result in a visible addition to a community or the region, every time you see it it can remind you of the joint experience.
