It certainly smells bad, in many levels. Just ask yourself what would happen if someone extends Child ; or it another subclass of Parent (instead of Child) is made.
It's hard to imagine a case that would justify this design (perhaps it exists, you could explain what you are trying to achieve). (Are you familiar with the factory pattern?)
In any case, to get a reasonable behaviour for such design I guess one should accept and embrace the coupling, even try to enforce it, by making the Child class final/sealed (impossible to extend) and thinking both classes as a whole. But then again, that could (almost surely) better be achieved with another cleaner design.