1st thought:
Assuming the capacitors you are using have very low ESR and inductance, I would assume that the ringing is due to lead inductance in the circuit. So use thick ground traces on the PCB and a single point ground type layout for the LPF.
2nd thought:
The ringing you see on the scope could be due simply to the ground lead of the probe. A way to check for this is to scope the ground point where the probe alligator clip is attached to. If you still see the ringing waveform, you know what the culprit is. There are special attachments for your probes that help eliminate the ground loop on the probe. They look like a spring with a small wire tail. The "spring" slips over the metal ring at the end of the probe providing a low inductance ground point.