Note that "gonna" is not a word. It is a how some people (with some accents) say "going to", but usually we never write this (unless maybe in a pop song). If you are very young and talking to a young friend, ok, but otherwise you might look a bit uneducated to write like this. (But, I am British, maybe Americans differ?) Anyway, this one is GRAMMATICALLY correct: "you're gonna have a book" = you are going to have a book However, this sentence sounds incomplete. Better: "When you arrive in class, you are going to have a book to read" "When you join the library, you are going to have a book every week" Or whatever. If you mean generally that you will get a book, then better: "you will have a book" / "you'll have a book"

In Black American English and some southern dialects, "you gonna" is common. Therefore, "you gonna" is common in rap songs. If you are trying to sound like a rapper, say "you gonna." "You gonna" is becoming common on the internet and in textspeak by people who want to look cool. However, the default, standard thing to write is "you are going to".

It is difficult because "gonna" is a nonstandard word, and when people are using nonstandard words, they are using nonstandard speech, which means they are using nonstandard grammar, too. So in effect you are asking "which is correct nonstandard English," or "which is correct incorrect English?" "You are going to have a book" is correct, standard English. "You're" is a standard contraction of "you are," so "You're going to have a book" is also correct. "Gonna" is a nonstandard contraction, or sloppy pronunciation, of "going to," so grammatically, "You're gonna have a book" is correct. The problem is deciding about "you." "You" might just be a careless shortening of "You're," in which case "You gonna have a book" would be correct." Or, it might be nonstandard grammar as well. Incidentally, we could go one step further, because "You're" and "You" can be shortened further, just to "Ya" or "Y'" "Ya gonna have a book." Once you depart from nonstandard English, you are adopting the language of some particular social group, and the only answer to what is "right" is to spend a lot of time listening and speaking to people who belong to that group.

I will, however, mention a song from the musical "South Pacific," entitled "Happy Talk." The song is sung by a character who is not a native English speaker and speaks nonstandard English. The lyrics to the recurring chorus illustrate "How you gonna have..." in place of "How are you going to have..." "Happy talk, keep talkin' happy talk; Talk about things you'd like to do. You gotta have a dream, if you don't have a dream, How you gonna have a dream come true?" https://www.youtube.com/watch?v=JXgmQDFhPjo

Thanks Gray! Believe you me, I will mark your words.