Green’s Dictionary of Slang

church n.1

[? misreading of chuck n.1 ]

a general term of endearment, e.g. my church, my dear.

[US]Matsell Vocabulum.
[UK]Barrère & Leland Dict. of Sl., Jargon and Cant.
[Aus]Crowe Aus. Sl. Dict. 17: Church, a term of endearment; ‘my church,’ my dear.

In phrases

do church (v.)

(N.Z. gay) to kneel in order to fellate another man’s oenis, pushed through a hole between two lavatory cubicles.

[NZ]W. Ings ‘Trolling the Beat to Working the Soob’ in Int’l Jrnl Lexicog. 23:1 64: When a man kneeled to do this [i.e. fellate an anonymous partner] , he was described as doing church or kneeling at the altar.