Consider the following from Grammar Bytes:
Two words, however, have incredible sentence power. Each and every are singular and can strong-arm an otherwise plural antecedent to become singular as well.
Watch what happens:
The cowboy and his horse drank their fill at the desert oasis.
Each cowboy and horse drank his fill at the desert oasis.
Every cowboy, horse, pack mule, trail hand, and cook drank his fill at the desert oasis.
Each and every will also change the verbs that have to agree:
Whenever a diner walks in five minutes before closing, the cook and waitress sigh and roll their eyes.
Whenever a diner walks in five minutes before closing, every cook and waitress sighs and rolls her eyes.
- Rules for Finding and Fixing Pronoun Agreement Errors
The key idea is to consider the unit the verb applies to. Your example is:
Every boy and every girl is/are happy.
Here, the candidate units are
- child, whether boy or girl; or
- a selection from "every boy", coordinated with a selection from "every girl".
In the first case, the unit is one child, so *every boy and every girl is happy. This would be the straightforward reading of the sample sentence. This is also the force of the quote above.
If we changed the reference to (say) coordinates, however, we can end up with the second candidate unit being natural. For example:
- Every X coordinate and every Y coordinate match(es).
If the context is that we are matching X1 with Y1, X2 with Y2 and so on, plural agreement works. If, instead, we're talking about any of the X coordinates matching with any of the Y coordinates, we'd revert to singular agreement.
Here's an example of plural agreement in print (emphasis, mine):
- Men have their faults, their humours, and their follies, it is certain; the ladies sometimes have theirs too; and my readers would little imagine, till it comes to a trial, how much every husband and every wife are what their help-mates make them.
- The New Christian's magazine
If they had used singular agreement, the quote would be referring to individual husbands and, separately, individual wives. By using plural agreement, the author brings into view the dynamic of the husband-wife 'marital unit', that both affect the other - but only the respective other.