I don’t think that’s what you’re really asking, though. What I get from your subtext is: "How do I sound good over these chords."

That’s going to be tough to answer in a short space. It’s also a complicated concept that can boil down to a simple answer. I like what Dave B said, and pianojazz man gives good info(although tri-tone substitutions would seem to be too difficult for you if you’re asking this particular question).

Most teachers will tell you the easiest approach is to figure out the chord tones and base a rhythmic idea on those notes. I prefer the jump-start approach: figure out a good rhythmic hook, and make sure it fits the notes.

All three of those chords are in roughly the same key of G major (there’s a little exception to that — I’ll explain soon), although a beginning player (which I assume you are) would typically expect them to appear in a different order: Am7 D9 G7. This is known as a two-five-one progression.

Warning: Theory (lite) ahead–

If you number the scale tones in the G major scale, you get (theory numbering is Roman, sort of, capitals denoting major and lower case denoting minor):
G=I A=ii B=iii C=IV D=V E=vi F=vii —— 7 notes, note 8 is same as note 1, up an octave.
That means the chords are (the way I re-wrote a ii V(7) I(7) progression (called "two-five-one" commonly). You see this progression all over jazz and related forms.

Regardless of the order the chords show up in, the simple thing to do is play a G major scale over all three chords, except on the G7, where you would flat the 7th, making it an F instead of an F# (important: notice that this makes the G7 in the major key of C, so the C major scale would apply to that chord). Once you have the tonality in your ear, you can play around with rhythms using the notes. Move on to the chord approach i described earlier.

The next important thing to look at is: How much time do you have to play an idea over this chord change? Honestly, it’s easy to play too many notes at a fast tempo and leave a listener cold. At a slow tempo, you have more time, but you have to make better use of it, because everything is more apparent to the listener. A better approach is to understand the underlying chord structure of the whole song or solo section, and figure out what rhythmic idea you want to convey to the listener. Then you can make sure it fits the note requirements of the chords at the tempo of the piece.

Whew. When you spit it out like that, it sounds hard! It’s really not that difficult. Get a teacher to show you how it’s done, and you’ll be making the changes in no time.