Although not an income tax expert, I am an accountant, and have dealt with other tax issues.
Generally, anything you give a charity counts is a tax deductible contribution. The church is not obligated to give out receipts, it is the obligation of the giver to keep track of the donations and have available proof of the donation. Unless they have good reason not to accept it, the IRS will treat any written record as proof, in other words a handwritten notation on a calendar that you gave $15 last Sunday will do.
Interesting sidebar: those green handshakes to the CO are not deductible by the giver and ARE taxable income to the recipient. Of course, who's going to prove that?