Hi zhifu,
A moderate amount of load capacitance (a few pF to a few hundred pF) directly applied to an op-amp output is generally problematic since it produces a second pole in the loop gain response before the 0 dB loop gain crossover, but putting something like a 10 uF load can often be done successfully because it nonlinearly drops the open-loop gain magnitude response and pushes its 0 dB crossover back in frequency where the phase shift is less. The nice thing about this is that you get the stabilizing effect of inserting attenuation in the loop gain without increasing the closed-loop gain. This allows the circuit to be operated at a gain of one, which is most often the desired gain. The only reason it works is because the op-amp is not ideal, and its open-loop magnitude response drops with the heavy cap load. The AD8031 is a popular op-amp in this application, and has been well proven to be stable with a 10 uF load at unity gain. I recommend that you use the AD8031 in a gain of one, with a 10 uF capacitor and 0.1 uF capacitor in parallel between its output and ground. (You can always change the 0.1 uF value or place additional smaller caps in parallel if necessary, once the 10 uF cap is in place.) This will give you a broadband low-Z source to drive the "GAIN" input.
Best regards.
--Jonathan