Which FAA regulations cover the certification of aircraft engines?
The relevant section of the FARs for engine certification standards is 14CFR33 - AIRWORTHINESS STANDARDS: AIRCRAFT ENGINES, with 33.31 through 33.57 dealing with reciprocating (piston) powerplants &amp; their testing requirements, and 33.61 through 33.99 being the equivalent for turbine powerplants.

There are also the 33 series Advisory Circulars dealing with such fun topics as how to comply with the Bird Ingestion Certification Standards (33.76-1A).