What datasheet for the AY-3-8912A are you using? The ones I've got specify a minimum write data pulse time of only 500nS (for example, see
http://www.ym2149.com/ay8910.pdf).
I've never had any problems writing directly to these devices from a 1MHz or 2MHz 6502 with the chip directly connected to the CPU bus and no wait states - working at 2MHz obviously hugely violates the write data pulse time but I've never had any problems with over a dozen different AY-3-8910's and AY-3-8912's, so I guess the data sheet value is very conservative. Either that, or newer versions are faster than the original devices. All the devices I've used have 1980's date codes on them.
If you are not getting any output from the chip, check the following first before you try slowing down your processor.
What combination of control signals are you feeding the AY-3-8912A chip? I've always used the following.
BC2 = tied high
BDIR & BC1 are normally low.
Write data = pulse BDIR high
Write address = pulse BDIR & BC1 high
I've never read back from the PSG but pulsing just BC1 high should make it output register contents on its data bus.
These pulses should be generated when the 6502 addresses the PSG and phase-2 is high.
Also, if the chip does not seem to be generating any output, remember that the analog outputs are current outputs, not voltage outputs. Without a resistor from the analog outputs to ground, the chip won't generate any output! I couldn't find a suitable value given in the data sheet but I recall using 4.7k resistors when I've used these devices - I'll have to check to confirm this, however.
Don't forget that writing to a register is a two-stage process, first you must write the register address, then you must write the data itself.
And don't forget that register 7 needs to be written to to enable the sound channels before the chip will do anything!
As a quick test, the following should generate an output on chanel 1.
Write 0 to reg 0
Write 4 to reg 1
Write 254 to reg 7
Write 15 to reg 10
I appologise if I'm telling you things you already know, but these points cover the problems I encountered when I first used an AY-3-8912. I hope you find them useful.
Edit - Another Idea
As you say there is no nead to read from the PSG, you could always use a latch to latch the data written to it and a monostable to extend the BDIR and BC1 pulses to meet the PSG's timing requirements. This would avoid slowing down the CPU and would still remain effective if you decided to increase your CPU's clock speed later. At high clock speeds, this would mean you eed to watch how often you write to the PSG - the CPU might have to wait until the previous write was finished but at 2MHz, the write pulse should be over before the 6502 can grab another value to write to the PSG
EDIT I see nyef also suggested this.