Get negative control voltage for a AS3310 chip
Sounds like an easy job for a linear, negative voltage regulator IC. 

Just like there's a whole world of voltage regulators that can give you +5 V from a + 12 V source, you can get -5V from a -12V source using the right regulator.

Something like the LM2990. 

Anyways, trying to grasp this AS3310 chip: It seems like an extreme specific one, and I honestly don't see why you'd need a chip that needs three different potentials (Vee, Vcc, GND), multiple voltage inputs (which you'd have to accurately generate somewhere else), as well as 11 (!) external components to generate such simple waveforms. Are you sure you wouldn't be happier with just a microcontroller generating these waveforms? Considering the timescales are all significantly larger than 1 ms, every modern microcontroller would be fast enough, and you could even get away without a proper DAC unit or separate IC, simply by PWM/chopping and proper low-pass filtering.