Is it possible to patch concrete stairs?
You can't just slap down new concrete. It will never bond. Some options:

1) They make bonding agents for this. Not sure how well they work.

2) vinyl patching compound. Probably your best bet for damages stairs. Not as good as new concrete, but might hold you over for a while. 

3) Epoxy. probably the best for small repairs. I use it quite a bit for small cracks and pits. 

Without seeing pictures, I'm guessing #2 is maybe what you want to try first.