When is the best time to pray to the Buddha?

Early morning and early evening.

Never.  Buddha is just a stone statue.  A false god made with humans hands.  If he ever lived, he is now 'stone' dead!!!!!!!!!

Are you completely crazy, and is it possible that no one in your house knows anything?

Do you pray to your supposed god, the one who has crooked legs, and a belly that hangs down?

Well, get your suitcase ready, you will meet him in hell, out there you will cry together!

8:14 PM.           

I won't click on that link but only God can receive and answer prayers, praying to something or someone called the Buddha is a form of blasphemy and will be punished in the last days.

So the answer to your question is never.

I don't know of any sect that prays to him directly.

Worth mentioning that the man himself didn't think much of prayer. Arguing that doesn't seem to be effective.