Orsman, The Dictionary of New Zealand English:
sook, n. and a. Also sookie, sook(e)y. [f. Brit. dial. sook a var. of suck, used as a pet name for calves (sucky-claf) or as a call to cows and calves (see EDD and ADD: see also EDD suck n. 19 a 'duffer', a stupid fellow: cf. OEDAS sook (1850), sookie (1838) a name or call for cattle, Sc. (usu. for a calf) and US (usu. for a cow).]
1. [AND 1941] A timid, soft-natured, or cowardly person, a sissy; esp. of a child, a cry-baby.
c1920 p.c. R. Mason. sookie used by her mother in the sense of cry-baby.
1933 SCANLAN Tides of Youth 155 And I saw Pat was a dismal failure because he didn't arrive in his brass buttons, and he looked a big sookie and wouldn't say a word [...]
[AND 1901] Timid, soft-natured; sissy.
1964 Weekly News (Auckland) 18 Mar. 58 The bys say they feel sooky wearing caps
1970 Listener 12 Oct. 13 Their attitude of tolerant resignation toward the sooky Maoris who are always getting into trouble [...]