Analyze the loop gain and try to adjust it towards a stable roll-off. If you need a specific closed loop bandwidth as well, most likely only an amplifier with higher bandwidth can solve the problem.
For a simple hand calculation, you can assume an open loop OP output impedance of about 30 ohm, as suggested by datasheet diagram TPC 4. If you sketch the bode diagram, you see a pole/zero pair created by the output RC load (lag/lead). The unity gain transition must occur at frequencies above the zero, so with AD825, Riso must be increased above 0.5 ohm even for a unity gain buffer.
Adding an output stage may be required to drive the intended output current. But it must be a class AB stage to avoid negative loop gain effects. It's lower output impedance gives also better chances to create a stable loop.