Nappy
1920s: abbreviation of napkin.
wiktionary
Probably shortened from napkin (but possibly a corruption of French nappe, since napkin is already a diminutive).
From nap + -y.
From Middle English nap, from Old English hnæp, hnæpp, hnæpf(“cup, bowl”), from Proto-Germanic *hnappaz(“bowl, goblet, cup”). See hanaper.
(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.)
Related to knap.
etymonline
nappy (adj.)
"downy, having an abundance of nap on the surface," c. 1500, noppi, from nap (n.1) + -y (2). Earlier, of ale, "having a head, foamy" (mid-15c.), hence, in slang, "slightly intoxicated" (1721). Meaning "fuzzy, kinky," especially used in colloquial or derogatory reference to the hair of black people, is by 1840. It also was used of sheep. Related: Nappiness.
nappy (n.)
British colloquial for "baby's diaper," 1927, from use of napkin in this sense. Related: Nappies.