I would encourage you to look at what the U.K. is doing. They have the Gift Aid system, where high-income earners can get a tax credit. But if you're not a high earner, if you give to charity, the charity will ask you, “Are you a U.K. taxpayer?” The equivalent to the tax credit is given back to the charity.
Some research has been done for HMRC by Sarah Smith and Kimberley Scharf on the differences in terms of individual behaviour with regard to how they perceive that type of indirect government support of charities versus a credit system.