Experiments:
I tried 1N4148. After connecting R2, output is not stable for a few seconds. After stabilized, small fluctuating exists. I added 25R resistors in front of capacitors, the circuit became stable. Fluctuating was not bad, but still worse than with unspecified 1N5819.
I tried MMBT3904 transistor (B-E) but it did not work at all. Probably it should, but I did not spend much time on this.
RC (=R3+C1 / R4+C2) of 5R+100nF stabilizes the circuit pretty well, but still the best known diode is not yet found. (25R+100nF works as well what comes to fluctuating, but takes much longer to find peaks naturally). I also tried 50R+10nF that should limit op amp current preserving behavior, but for some reason 5R+100nF is more stable than 50R+10nF.
In the end, with unknown 1N5819 + RC circuit added, ADC readings are rock solid. I know now what diodes I will buy and try to find as good candidate as orderable version.
sw guy