Am9 contains fives notes: A, C, E, G, & B. Ukes only have four strings, so we must drop a note to play this one. Some options:
2002 (no G---this chord is "A minor add 9", Sarah's post #4 chord, Jim's post #7 provides alternate voicing)
0002 (no A---leaving the root note to the imagination often works well in context)
2032 (no E---same notes as Bedini's post #8 barre chord and Bill's post #9 voicing)
2432 (no C---this will leave it to the listener to figure out it's a minor chord)
0000 (no B---this is Am7)
Your ears should help you find out which of these options (or which combination of these options) will work best in context. Strumming the open strings (playing Am7) and fretting the 2nd fret of the outer strings (for 0002 or 2000) as the mood strikes will play all the notes of Am9 without twisting up your fingers too badly. Have fun!