I can truthfully use this sentence! <3

How about: 'сестрійнок' (nephew from the sister's side) & 'братанок' (nephew from the brother's side).

These terms are more specific, and you know whom you're talking about.

'Племінник' is a general term for 'nephew'. (I've used all three terms during my lifetime. All are acceptable and used.)

How about "небога"? Imho it's a quite classical definition.
http://sum.in.ua/s/nebogha