CM7 - C, E, G, B
C7 - C, E, G, Bb
Cm7 - C, Eb, G, Bb
Caug7 - C, E, G#, Bb
Cdim7 - C, Eb, Gb, A.
Why Does Cdim7 contain an A and not a Bb?
C°7 actually includes a B doubleflat.
A major seventh above C is B and a minor seventh above C is B♭. This means that a diminished seventh above C is actually B♭♭, which is enharmonic to A.
But the seventh is not A, because A is just a sixth above C. A is enharmonic to B♭♭, but since we want the seventh above C, it must be B♭♭, not A.
But it gets more interesting: since fully diminished sevenths are just stacked minor thirds, they can be spelled four different ways, with each pitch as root; we say that these chords are enharmonic, just like we say that A is enharmonic to B♭♭.
This then means that C–E♭–G♭–A is a diminished seventh chord, but with A as the root: A–C–E♭–G♭. If E♭ is the root, we'd rather spell it as D♯–F♯–A–C. If G♭ is the root, we'd spell it as F♯–A–C–E♭.
These chords all sound the same as C°7, but they are spelled differently.
Other answers have pointed out that it's a B♭♭, not an A. To answer the question "why not a B♭":
The chord in question is the chord of the diminished 7th. As David Bowling and Richard have stated, if the root is C, the diminished 7th is B♭♭.
The chord is also called the "diminished 7th chord". This name and its chord symbol Cdim7 are perhaps confusing. I don't know if this is what you thought, but, just for the record, "Cdim7" does not mean
It's not a [ diminished triad ] with a seventh. It's a chord of the [ diminished seventh ].
A Cdim7 chord is actually spelled C-Eb-Gb-Bbb, where the interval from C to Bbb is called a diminished seventh. The interval from C to A is a major sixth, but sometimes you do see people spell Cdim7 as C-Eb-Gb-A for convenience to avoid the double flat, it is just technically incorrect. This chord is sometimes called a fully-diminished chord, in contrast to a half-diminished chord. A half-diminished C chord (Cmin7b5, C-7b5, or C∅) is spelled: C-Eb-Gb-Bb. These are often found in ii-V-i progressions in jazz.
Adding a little to the others. Cdim7 cannot contain a Bb note. Bb only produces a minor 7th from the root. To make it a diminished 7th, the space between root and m7 needs to be one semitone smaller. That's the reason it gets called Bbb. It sounds just like A, but since C>A is a M6, that wouldn't be correct if the chord was to be called dim7.