Does it mean that the timing to be happy is rare, so that we should seize the day and be happy?
Could anyone help clarify, please?
It means, you should not put off (delay) being happy. If you followed this saying, then you would choose to be happy right now. Tomorrow, you would once again be in the "right now" and would again choose to be happy.
Conversely, if you decided "I will be happy tomorrow," then you are choosing to be sad today. If you always followed that maxim, you would always be sad.
Obviously there is more to being happy and sad than just the choice (well, I'll leave that one to psychologists...), but the point is that one should strive in each moment to be happy, as there is no value/benefit in delaying happiness.
Thus, "There is no better time to be happy than now" is a call to action, telling the reader to take advantage of the present to be happy, and not to put off one's happiness to the future.