Is the plane going to be doing aerobatics? Then the camera mountings have to be set up for high g-forces and the install will have to be signed off by an FAA inspector, or the pilot could lose his license. Not to mention his life, should the thing go flying around the cabin and hit him in the eye or head while maneuvering, or interfere with the rudder pedals, control cables, or stick travel.
If it is a gentle, no-stunts flagpole-circling cruise around the pea patch we’re talking about, you *might* get away with gaffer taping a small lipstick camera or ice cube POV type tightly to some part of the cabin structure. You’d run a cable from there with more gaffer tape to a recording deck tightly strapped into the second seat.
Forget suction cups.
A lipstick cam is good for this because it has small size and low mass, can be put almost anywhere with confidence it will STAY there. Don’t even consider a handicam for this: it will become a deadly missile in the cabin under sudden accellerations.
You should probably consult the local FAA safety inspector regardless, before proceeding.