Green’s Dictionary of Slang

daylight n.2

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

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[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.