Dand, a Glasier woud work very good, no over-penetration. But be aware you will have to sight-in your weapon ( handgun or rifle ) for that round, since it is light and fast, will most likely have a very different point of impact. They are loaded "hot", though. Certainly not clandestine.
I think the best round is sub-sonic. A .22 standard velocity, out of a long-barrelled rifle is pretty quiet, expecially if the muzzle is well within a structure. At night, escpecially late, one low-level gunshot generally does not cause much concern...might wake up people, but they will not be sure what exactly they heard, nor where it came from, etc. More then one, different story. In a populated enviroment, I think the best way is a sub-sonic .22 . I did some testing a short time ago, even a .38 special wadcutter target round, fired from a Handi-rifle, makes considerably more noise then the .22 .
For extreme quietness, the .22 super colibri from a short barrel ( 16") rifle is best, hardly noticable from a few feet away, but it deffinately lacks power. For a pit ( short-hair, not a really big dog ) a heart-lung shot with the super colibri may do the job, not a quick kill, which is ok, let the dog make it home to either die, or cause a big vet bill to the owner. Whatever you do, keep your mouth shut, no need for "fieud", which a good person can never win against trash ( slashed tires, "keyed" paint, etc.).