(lands of) Unakeris 1556 x 1585 RMS v no. 843 [part of the barony of Kirkcaldy; see KDT, KXY Introduction for more details]
(lands of) Uneakeris 1594 RMS vi no. 75 col. 3 [see Muirton (of Kirkcaldy)]
Unaikeris 1636 RMS ix no. 539
While the second element is Sc acre ‘acre’, the first element is obscure. If it is the negative particle un-, it might possibly express a negative quality of the following noun (in this case ‘bad acres’), similar to G do- (for which see Dolly DFL and Devilla CUS). I can, however, find no such usage in DSL.
This place-name appeared in printed volume 1