Now that I've thought about a bit, I'll back off on the statement about bypass caps not adding to stability. I now see where you are coming from.
I will stand by my statement that the term "coupling capacitor" is a misnomer. The purpose of the cap is to isolate the two stages from the stand point of DC. If all you wanted to do was couple two points together to pass an AC signal you would just use a piece of wire. There are such direct coupled circuits that don't use capacitors. If the output of one stage is at a different DC potential than the input of the next stage, then you use a cap to block the DC. Otherwise you would dipense with the cap and just wire them together. So they really should be called DC blocking capacitors. No big deal, just thought it might be of interest to some.
I will stand by my statement that the term "coupling capacitor" is a misnomer. The purpose of the cap is to isolate the two stages from the stand point of DC. If all you wanted to do was couple two points together to pass an AC signal you would just use a piece of wire. There are such direct coupled circuits that don't use capacitors. If the output of one stage is at a different DC potential than the input of the next stage, then you use a cap to block the DC. Otherwise you would dipense with the cap and just wire them together. So they really should be called DC blocking capacitors. No big deal, just thought it might be of interest to some.