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Sub-Sonic 1060 ammo should cycle... might require a small tune to the spring... or just buy a soft Sub-Sonic spring and change it back when you return to HV's. Quiets probably won't cycle, although I did build one gun specifically for Quiets... and then could not get them to shoot... 1.5" at 50m is not acceptable... same gun with SV's would do 1/2" at 50m.
So to answer the question, no, you're doing absolutely NO damage to your rifle shooting CCI "Quiet-22". However, several ammo types fall under the "subsonic" category. Any ammo under about 1120 fps is "subsonic", and many ammo types fall just safely under that level. The ones that come close, but don't exceed (ie, CCI SV @ 1070fps) are considered...but not always called "standard" velocity. These are likely to cycle the action of your model 60 perfectly, as would "high velocity" ammo. (the highest velocity ammos can damage the bolt buffers if used long enough) The CCI Quiet, CCI CB longs are in a lower-speed category around 700 fps, and lack the juice to cycle a semi, which is why cycling the bolt manually is req.
You may know all of that, but unless I knew my neighbors would have an issue with it...I'd probably try some of the 1050fps-ish velocity stuff. Being the charmer that I am ( ) I'd probably invite them over to try it themselves...see if they think it's "too loud". They might enjoy that, and be more open-minded going forward.