I didn't know, so I had a look in the Oxford Dictionary and found they are acceptable forms based on the word normal. Of course, I wanted to know more about it, because I would never use the word 'normalcy', and I found a discussion in which it was thought that 'normalcy' is an American usage and 'normality' an English usage.
On the other hand, the online Macquarie dictionary (Australian English) says:
normalcy: noun the character or state of being normal; normality: back to normalcy.
The Online Etymology Dictionary says:
Language Corner has more about the Warren Harding connection, saying the word was avoided in the past in the US but is now acceptable.
After consideration, I think I'll stick to using the word 'normality'.