Every fingering that fits a hand
x30330
open · no 5
x30310
open · no 5
x30056
easy
x30350
easy · no 5
x35330
moderate · barre
What is true of it
C9 is C, E, G, B♭ and D — 1, 3, 5, b7 and 9 counted from C.
On an instrument that cannot reach all 5, the 5 and 1 go first, in that order.
The easiest of the 5 fingerings below is x30330: 3 fingers, held at the 3rd fret.
2 of them use open strings, which is what makes a shape quiet to change to.
1 of the 5 need a barre.
It leaves out the 5. 6 strings cannot carry 5 notes, and the 5 is the one this chord can lose without changing what it is.
1 string stays silent.
Where its notes are on the neck
The brass dots are C, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
C9/E
010010
C9/G
310010
C9/B♭
x10010
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.