CRJ-200 pilot reported during climb the #2 engine started to vibrate and the flight crew heard two loud bangs. The flight diverted to the nearest airport.

Narrative

T/O on XXL in ZZZ. climb was normal up to 24000; (I had to constantly readjust N1 since we had no Speed Switch). At 24000 feet when I adjusted N1 the right engine started vibrating and we heard 2 bang noises; followed by Low oil Pressure and Low Fuel Pressure and a Red Master Warning. and the gauges decreased for the right engine.Capt called out Engine Failure; and I called for the checklist. Shortly after; The engine resumed to normal settings. Capt [requested priority handling] with Center. Capt initially attempted to find the relight QRH procedure; but when engine resumed; he continued in the QRH to find the proper procedure. Meanwhile he communicated with ATC and Dispatch. There was a brief mention about returning to ZZZ; however by the time the QRH procedures were completed and Dispatch concurred; we were about halfway between ZZZ and ZZZ1 and the nearest suitable airport was ZZZ2. As we began our descent towards ZZZ2 the engine began to vibrate again for a few seconds; but once again it resumed to run normal. On approach to runway XYL; as I adjusted the power; the engine vibration was felt once more. At this point Capt Called for a Go Around; which we executed and he called for the controls. We proceeded with In-flight engine shut down/per QRH; and the Capt executed a Single Engine Landing at ZZZ2.