I a trying to burn an audio CD, but I keep getting burn errors.
That is probably because my minimum burn speed is 16x (as detected by Windows Media Player).
How can I reduce the burn speed to 2x or 4x?
As a musician who records music and produces some, this is something I've looked into in the past. When we provide a master CD for duplication, it is always asked to be burnt at the slowest speed it can. It has never been decreed that it must be at a given speed though.
Simply, the issue with fast writes is that not all players can read them. But technology is constantly improving and whilst I'm not saying you won't find examples where this issue still occurs, it's now quite rare (based upon my own experience).
Another factor is what you're burning too. If you go for an non-trusted poor quality disc, then you're likely to have other problems as well. As long as you're burning at the slowest speed and that speed is within the range that disc supports, you should not see any problem.
The actual limitation is down to hardware. Unless you find a way to upgrade the firmware then no, you can't.
To address some points you make in the comments having a lower rate of burn does not mean less errors! In fact, it was believed (and I can't find a source) that 16x speed was the "best" to burn at as it could be read by the majority of CD readers
You may find second hand CD burners which will suffice for your needs (forcing the slower write).
Try different brands of CD, not just a different disc from the same spindle/pack.
Try to burn another set of songs to see if one of the files you're burning is actually faulty and maybe the software can't read the data and is throwing an exception but you're seeing a more generic error message.
Try a different CD burner.