The 7135 datasheets (Intersil, TI, Maxim, Microchip, Teledyne) have no clock requirement spec:
"The clock source should be free of short-term phase and frequency jitter during the conversion period, but long term stability is not critical."
"The clock used should be free from significant phase or frequency jitter."
There's four different oscillator types in the datasheets- comparator or logic gate and xtal or RC.
I see Pierce oscillators with Schmitt triggers or buffered or unbuffered CMOS logic gates.
I couldn't anything on oscillator design wrt jitter and phase noise, well it's an issue in the RF domain.
You have a sine-wave and at some point need to convert to digital.
For low jitter, I imagine you want consistent switching thresholds- so a clean power supply, low noise stable threshold detection and some hysteresis?
Schmitt triggers give a fast-edge but threshold voltages are imprecise, and David you say noise is poor.
Just trying to understand the oscillator side before looking at what the A/D needs.