General aviation pilot reported a near miss with another aircraft during climb from a non-towered airport in visual conditions on a training flight. The pilot and the instructor were distracted with the avionics; then the pilot maneuvered to avoid the traffic conflict with two aircraft.

Narrative

I was a trainee pilot on my first G1000 training flight. The instructor asked me to activate the autopilot once we reached 800 AGL as we climbed out of 47N from RUNWAY 25. We had planned to use the NAV mode and VOR on the CDI to navigate to the SBJ VOR. I had my head down (and I believe the instructor did as well) looking at the G1000 when we got an alert 'Traffic; 1 mile; 1 o'clock; same altitude.' I looked up and saw another aircraft coming towards us. I thought that if pushed too hard on the yoke to maneuver away; I might overpower the AP and activate a runaway trim situation (I completely forgot about the CWS button function to prevent that from happening). I very gently applied pressure on the nose to reduce our rate of climb. The other aircraft turned to the right. We were then alerted to a second plane which was very close behind him and at our 12 o'clock position; also at our altitude and also 1 nm away. At that point; I turned off the autopilot and lowered the nose to avoid the other plane. This all happened in the space of about 45 seconds.What I learned was that it's not a good idea to turn the autopilot on below 2;500 ft AGL in case you have to avoid other pattern traffic (especially for pilots new to the G1000 who haven't gotten that CES muscle memory). I also learned that anyone who puts his/her head down in the cockpit should announce it; just like we do for the positive exchange of controls.