Green’s Dictionary of Slang

a nap, a snooze, a brief sleep.

1912		B. Fisher Mutt & Jeff 19 Jan. [synd. cartoon] I guarantee my pupils to hypnotize just as well as me. Just look your subject in the eye, use your hands thusly, and repeat the mystic word ‘ziz’ [...] Zizz! Zizz! Zizz!
1941		Tee Emm Aug. 17: He could not have caught our Pilot Officer Prune at three o’clock one afternoon having a zizz full-length on a mess settee [OED].
1947		D. Davin For the Rest of Our Lives 310: You’d better get to your bivvy and have a bit of a ziz.
1968		Manchester Guardian Weekly 11 July 14: The others retire to have a ‘zizz’ or unpack their luggage.
1972		K. Bonfiglioli Don’t Point That Thing at Me (1991) 53: I had a little zizz until Martland telephoned.
1989		T. Blacker Fixx 20: There he had what he insisted on calling a ‘zizz’ in his favourite armchair.
2005		Guardian 11 July 10: Members went on using [...] Charles Morgan’s old chair [...] for an after-lunch zizz.