Using the TPS65131EVM-839 board, I find the negative output is unstable with varying load. Using a programmable load, stepping between 10ma and 50ma with 4ms period, I observe the output voltage oscillate. I've attached a screenshot, but what is not clear from this static image is that the "sine" looking portion of the waveform is varying with time from cycle to cycle. I first observed this in my application, where this regulator is powering a number of opamps. Driving those opamps near rail-to-rail with a 1kHz signal causes VNEG to oscillate at the same 1kHz rate.
VPOS is better behaved, although I see slight oscillations--observe the "pip" at 3ms in the VPOS screenshot I've attached. Again, this is varying with time, but this is not clear from a static image.
Since the common cause for these type of issues is layout, I've tried this same experiment with the EVM board, with similar results. So, unless the EVM layout is also suspect, this is probably not a layout issue.
The only change I have made to the EVM is to change the output voltage to +/-12V by changing R3 to 1M, R2 to 110K, and R5 to 1M.
Should I be able to get a non-oscillating output with varying load?