Nicht at Eenie was a book by Iain MacNab, published in Edinburgh in 1932.  I have never seen it, but it is referred to (by title only) in a number of files in the Digital Tradition, for example:

KATIE BEARDIE
THERE WAS A PIPER HAD A COO

I presume that it was a collection of Scottish children's songs; there was an Iain MacNab, a book illustrator and wood-engraver, active at that time; perhaps the same person.  That's all I know.

Malcolm