In addition to having a volume control, it's also necessary that an audio chip have a means of forcing a waveform generator to produce a DC output, it's necessary that setting the volume be quick, and it's necessary that the volume control be linear. On the SID chip, I think there's a "test" function that can be used for that, and if not I think setting a PWM width to maximum at a high frequency and passing that through a low-pass filter should yield something that's basically a DC level.
I don't know of any way to make the AY-3-8910 wave generators produce a solid "on" signal. The volume control is by design not linear. If one didn't mind limiting volume to 1/6 of maximum, it might be possible to program one of the channels for a maximum-frequency square wave (32,000Hz) and amplitude-modulate that, but the even if one used a translation table the non-symmetric distribution of output steps would likely make it impossible to get good results. Using multiple generators could improve overall volume, but would require storing four stores or six to the I/O port to select the first channel amplitude register, write a value to it, select the second channel output register, and write a value to that.