People like to give and you should give them every opportunity to do so, and in a variety of manners. From working with many ministries, there are multiple ways people can become a part of your team, outside of financial giving.
Knowing what you know about a potential partner, you can ask for 1 of 3 things, typically people can always give at least one. You can ask for: 1- a specific financial gift, 2- a commitment of prayer for 12 months, or 3- becoming an advocate, providing a list of 10 people they could personally connect you to as potential financial partners.
This process of asking for another commitment can have many benefits. It can give people an "out" if they don't feel comfortable with financial giving. And it can often lead to deeper relationships with those partners if they choose to commit to prayer or as an advocate.
As a rule of thumb, the prayer commitment is the lowest barrier, but surprisingly, that often leads to stronger partnerships over time. As some prayer partners who barely know you will actually pray for you, this will lead to an incredible prayer support team surrounding your ministry, and even possibly financial partnership at a later time. What a blessing to gain a financial partner with whom you have already built the relationship!
For more on asking for commitments, check out the e-book, How to Get a Generous Response (Almost) Every Time You Ask.