Is it correct to say "The boys shall go camping if it does not rain"?

When it comes to language, there are grammatical rules and then there is popular usage. They differ quite often in a world language such as English.

"The boys shall go camping if it does not rain" not only sounds a bit formal and old-fashioned to me (compare the rather literary phrase "you shall go to the ball!" in the Cinderella story). I too know about the formal rules of the future tense in English, namely "I shall, you will, he will, we shall, you will, they will), but even educated people don't stick to these rules and will say "I will, we will" rather than "I shall, we shall" when talking about the actions they are going to do in the future. To me, "shall" comes with a bit of determination, as if the action is a little against the odds. Personally, I wouldn't say "The boys shall go camping if it does not rain", I would say "The boys will go camping if it does not rain" instead.

As for "The boys could go camping if it does not rain", this is also possible in colloquial parlance rather than the more grammatically correct sequence of tenses "The boys could go camping if it did not rain", but be aware that "could go camping" hasn't the same meaning as "would go camping". "Could" means that camping is one choice among several for the boys, while "would" implies that the consequence of there being no rainfall is that the boys will definitely go camping.

Hope that makes sense.

try "would go" or "will go" and doesn't rain