The correct spelling is "raining" but yes, that would work but isn't what you'd usually say. You could also change it to "It's probably going to be raining tomorrow morning." or "It will probably rain..." or "It will rain..." The problem with "It will rain" or "it will be raining" is you're predicting the weather with certainty. So although it's grammatically correct, it's logically wrong. You should say "It will" for things that are certain or almost certain. "It will be Friday tomorrow." "You will be cold on your way to school if it is raining in the morning." "In the desert, it will be hot in the middle of the day." "It will probably rain tomorrow." "You should close the window in case it rains over night." "The weather forecast is calling for rain in the morning." "It's getting cloudy out. I think it's going to rain soon." "I'll be ready for the game tomorrow, but it will probably be raining in the morning."

It's going to be raining tomorrow morning or there's going to be rain tomorrow morning. Well on the first one you're saying probably which means you're not entirely sure. On the second one you sound sure of it.

Both of your statements are the same because both of them report news about weather not for sure. If you are sure you should say: it is raining tomorrow.

I usually advise my student to use to be going to,for probable future. You can say it is going to rain tomorrow .

"It will be raining tomorrow morning," works but it might sound a little stiff, a more relaxed version may be "It will rain tomorrow," or, "It will rain in the morning," though if this is assigned homework I'd stick with "It will be raining tomorrow morning."