I've given introductory lessons to several of my friends' kids. Before I discuss any notes or show any beats, I give them the following exercises: Alternating single strokes between limb pairs (not just the hands, but the feet too, such as between the right hand and right foot); and unison strokes with similar limb pairs.
This comes in handy when dissecting beats. I will have explained the reasoning behind these exercises: When, for example, it's time to play a left-handed 16th note on the snare between right-handed 8th notes on the hat or ride, it's just three alternating notes between the hands.
When it's time to discuss simple beats, I break out some Beatles, Stones, and Cheap Trick. In addition to using 8th notes on the hat, I show how each beat can be played with quarter-note and offbeat eighths, not only on the hat, but the ride, and alternate surfaces such as a cowbell or floor tom. So each beat has 12 potential feels. After that, I show them that most rock is simply a matter of mixing and matching these building blocks.
With motivated students, this method has yielded strong results in two or three lessons. Once they're on their way, I recommend "Realistic Rock" and "Stick Control" and suggest that they find a real teacher. On a few occasions, those teachers have told me (or the kid's parents) that they are shocked by how advanced the student was.