Well, "deep" usually means low frequency, so all you need to do is slow the loop down.
Oh, but then, you said,
"I've tried different frequencies, but it does not sound that much different."
So the problem now is that we can't really tell what fault you have with the existing sound. That is key to improving it...
You now have a "sawtooth" wave, you could make it a "triangle"...
void buttonBeep(){
for (int j = 0; j < 124; j++) {
for (int i = 0; i < 124; i++)
analogWrite(DAC0, i);
for (int i = 124; i >= 0; i--)
analogWrite(DAC0, i);
}
}