Generally, rafting and kayaking are a year-round activity, with a break for the monsoon season. However, if you are more of a beginner in both activities and don't feel too sure about yourself in the boat, even with a skilled instructor, try to avoid first months after the monsoon, September and October.
Rivers are still extremely full during these first months, currents are strong and waters rather deep. You'll definitely enjoy quite a pleasant calm swim in spring. On the contrary, choose the immediate months after monsoon for some harsh kayaking and rafting action. In any case, whatever time period you choose, remember that the rivers in Nepal generally have strong character, so be well-prepared!