My app contains a custom control that copies the behaviour of the iOS standard keyboard.
I can successfully play the system keyboard click sound with this code:
The url below could help with finding proper sound: https://github.com/TUNER88/iOSSystemSoundsLibrary
As of October 2019, these are the sound IDs
Press Click - ID: 1104
Press Delete - ID: 1155
Press Modifier - ID: 1156