Are "eery" and "eerie" equally acceptable spellings?

Solution 1:

As a well-read native speaker, I've never encountered "eery" until this question. Despite its apparent inclusion in the Oxford English Dictionary I would always change it to "eerie" in (for example) an editing job.

So to answer your question very literally, no, they're not equally acceptable, though they may both pass the minimum bar of being correct at all. Quite likely, the more formal the writing, the less acceptable is the "eery" spelling.

Solution 2:

The Oxford English Dictionary gives both.

It’s of Scottish origin, and probably derived from ‘argh’, an adjective now limited to regional dialects, and meaning ‘cowardly, pusillanimous, timid, fearful’ and also ‘inert, sluggish, lazy, slow, loath, reluctant’. ‘Eerie’ and ‘eery’ are just two of the word’s historical spellings, of which the earliest is ‘hery’.

'Eery' has been in use since the seventeenth century. ‘Eerie’ does now seem to be by far the most common.