How to hook up a subwoofer with an integrated amp?

It depends on the inputs accepted by your sub. I assume your sub will have separate inputs for the left and right channels, and it will somehow combine the signals internally into a mono bass (sound) output.

The Avatar appears not to have a line level output. It does have a tape out, but its gain is not regulated by the Avatar's volume control. The good news is that you have a volume control on the Cary. So, one way to go would be to connect the sub's line level input to the Avatar's tape output and use the Cary's volume control. With this, the Avatar's volume control should be turned up to a unity gain level to match levels between the sub and the main speakers. The primary drawbacks of this setup would be the inconvenience of using the Cary's volume control instead of the Avatar's and also the need for potentially long interconnect cables from the Avatar to the sub, possibly resulting in signal loss or degradation.

If your sub accepts the output of a power amp, i.e., speaker signal, then you could run a pair of speaker cables from the Avatar's output to the sub. This would be in parallel (electrically parallel) to the existing cables running to your Sonus Fabers. Depending on where your sub is located, you could run speaker cables from the Sonus Fabers' terminals to the sub instead. If you do it either of these ways, I would recommend hooking the speaker wires to the Avatar's four ohm tap to begin with. (The Grand Piano's are rated at eight ohms, but the effective load will drop when you add the sub to the circuit.) The primary drawback to this setup is that the signal to the sub may not be as perfect since it has gone through the Avatar's power amp stage. Potentially, the power amp may color the bass frequencies, and/or the bass frequency signal sent to the sub could be colored by the interaction between the amp and any impedance variations in the Sonus Fabers at the low end. Personally, I would choose the tape output method. Good luck.

Thanks James for your input, especially with the tape out. Unfortunately, my Cary (303/100) doesn't have a volume control (unlike the 306), therefore the tape out option may not work.

So, between using the Y adapt and running parallel speaker cables, which one is lesser of the evil? Or the parallel run, besides the drawback that James mentioned, what about cross over concern sonically? i.e. say the subwoofer's cross over will fiter out any signal above 80Hz, but what about the existing speakers, since there is no cross over that "tells" them not to drive below 80Hz. Would that be a concern, especially within the frequency range of, say 40 to 80Hz, when BOTH the SW and the speakers are driving together. Any inputs? Anyone?

I would suggest running Y instead of speaker cables.
Since most preamps out there with 2 sets of output which the design just basically "Y" inside the chassis anyways, I don't think Y-ing the line level signal will accfect the sound as mush as Y-ing the speaker cable signal.

Sorry about the mistake with the Cary. I read a review of the 303/200, and it seemed to have a volume control.

In this case, I would prefer using the parallel speaker wire to the sub. If you use a splitter placed at the output of the Cary (or the input of the Avatar), you have no control over the volume presented to the sub. With unity gain, the sub is likely to be too loud, out of balance with the volume of the Sonus Fabers. With a parallel speaker wire configuration, the Avatar's volume control would work for both the speakers and the sub. (The sub should have a volume control intended to match the sub's volume with the main speakers' volume for first time setup use.)

With respect to the crossover, many subs have a crossover control, so that the sub will operate at frequencies where the main speakers are unable to perform. If your Grand Piano's give up below, say, 30 Herz, then the sub should be set to operate below 30 Herz only. In practice, speaker and sub frequency responses tend to slope off, not start or stop in cliffs at specific frequencies, and there will be an overlap, so you might want to adjust the setting so the overall effect of the combined speakers and sub is smooth.

Some subs have a phase control, too. This is used to manage any cancellation or reinforcement of the speakers and the sub where they overlap. For example, if the sub is out of phase with the speakers, it will tend to cancel out the speakers' output for the frequencies where they overlap. If they are in phase, there will be reinforcement. Personally, I prefer to set the phase so there is reinforcement, then I lower the sub's crossover frequency to reduce the overlap until the output is as smooth as possible. Good luck.

Here are a few ideas from ACI on hooking up their subs.

Good luck