need an opening for black against openings other than e4 or d4 as white

1.c4 e5 Nc3 Nf6 g3 Bb4 is a solid choice.
Although who knows what white will play after 1.c4 at certain ratings, so just in general e5, Nf6, bishop outside the pawn chain at c5 or b4, and then d6 is solid against a lot of stuff.

Against 1.Nf3 I'd just try to transpose into the opening I want against 1.d4. There are a lot of transpositions and options for both sides, but this is the advice I'd offer for you. If your usual opening is not possible, do a semi-slav or old Indian setup.

Against 1.g3 you have even more options. Same advice for 1.Nf3.

Semi Slav type of setup

Old Indian type of setup

 
Notice all the standard opening principals still apply. Put a pawn in the center, develop quickly, castle.