Seth Jeffery is correct: "Every boy and every girl is happy."
As he pointed out, "every" remains singular, hence creating a compound sentence, with two subjects. I would parse it this way:
- Every boy is happy and every girl is happy.
- Every boy and girl is happy.
The first one, "Every boy and every girl is happy." Is a little too wordy. I think it can do without the second "every". I would let the second "every" be implied in that sentence. Essentially you're saying that the entire group of subjects is happy. Therefore the singular "group" is the implied subject.
You might also say: "The boys and girls are happy." That generally covers all of your subjects together as a plural, if you prefer to word it as such.