Yes, small-diaphragm condensers are a good choice for pianos. (So are large diaphragm condensers and ribbons).
The choice of microphone is based upon the role in which the instrument plays in the song/tune.
Is it a solo piano track, a jazz trio, a rock song, a pop song?
You also choose the microphone based upon the conditions (perfectly tuned studio or a room with bad reflections or a room that gets a lot of outside (traffic, refrigerators, neighbors, etc.) noise.
What are the parameters for this recording?