Green’s Dictionary of Slang

(US) to provide someone with an alibi.

1929		D. Hammett Red Harvest (1965) 67: ‘Damn it, Peak, [...] you told us before that you were with him at the bar.’ ‘Yep, I did [...] But I don’t know no reasons why I’ve got to cover him up nowadays’.
1939		Howsley Argot: Dict. of Und. Sl.
1943		R. Chandler Lady in the Lake (1952) 216: You covered the girl up. You were in love with her still.
1958		R. Prather Scrambled Yeggs 121: there wasn’t much of a try to cover it up.
1960, 1975		Wentworth & Flexner DAS.