Hello vivalite,
the 337 is wired-up using a virtual ground and this does not help with stability. I would try a 10u electrolytic in parallel with D33, which of course will send the opamp off the roof if you dont isolate. I would insert a 470R damping resistor at the opamps' output, which combined with the above capacitor will further filter out broadband noise.
It would also not hurt to slow down the opamp by connecting a small ceramic cap across its feedback.:wink: