I have tried to regulate the output voltage to be exactly -10V using the application circuit in the datasheet of AN79L10N on page 10 at https://www.ortodoxism.ro/datasheets/panasonic/SFF00006CEB.pdf .
The voltage closest to -10V that I could get to is -10V. Is there any way of getting closer to -10V? Thanks!
The adjustment parts allow you to increase the output voltage of whatever the IC has as a voltage (from 9.6V to 10.4V). You cannot decrease the voltage.
The adjustment parts ruin the excellent voltage regulation of the IC.
If you want an excellent adjustable negative voltage regulator then use an LM337.
I've taken a look at the 1N4740A zener diode. Apparently it has an error of up to 5%, which basically has the same regulation range as the -10V regulator.
An error of 5% means it can be between 9.5V and 10.5V and 10.1V is only 1% error so you've got a good one. Your meter probably has a tollerence of 1% so it could be between 10V and 10.2V.
I've taken a look at the 1N4740A zener diode. Apparently it has an error of up to 5%, which basically has the same regulation range as the -10V regulator.