Green’s Dictionary of Slang

daylight n.2

(Ulster) the minimum, anything, e.g. don’t believe daylight out of him.

[Ire](con. 1970) G. Moxley Danti-Dan in McGuinness Dazzling Dark (1996) II i: I wouldn’t believe daylight out of you. [Ibid.] II ii: He’s a lying bastard Dan. Don’t believe daylight out of his mouth.