Filtering capacitor only adds noise in a rail-splitter
As @brhans said, most of opamps become unstable in unity-gain configuration if they drive capacitive load. That is the case, when you put large 10uF C2. According to TL072 datasheet, there is 128 Ohm output resistor, which makes RC-circuit in conjuction with C2. It makes additional phase shift, which at some frequency converts negative feedback into positive, leading to oscillation.
Why do you want to use C2?

If the purpose is to additionally filter noise, then, as @brhans suggests, use resistor in serise with C2. Yes, it will increase DC ouput resestance of splitter, but it will decouple large capacitance from feedback looop and removes oscillation. Also, you can select opamp that is 'able to drive unlimited capacitive loads', AD826, for example.