Gyroplanes unlike fixed wing or even helicopters have yet to get in a larger scale or size other than that of the first versions of early gyroplanes. All sport aircraft started as small aircraft but airplanes and helicopter kits are now available with greater loads, ranges, seating capacity, speed and even aerobatic airplanes. What does this have to do with engines? You do not get performance without the power to create it.
Sometime around 2004, I think, I attended a forum at Sun Fun on the CarterCopter given by Jay Carter and his flight crew. Jay made known that when designing his ship he knew about how much horsepower he would need to reach his design goals. This left him with an engine choice of a turbine or some high performance reciprocating engine. Jay went searching for a possible alternate in an automotive engine and found his gem in a Corvette racing engine. In a horsepower/weight/cost ratio Jay found the available horsepower to be much cheaper than a comparable turbine and he would be able to handle the weight penalty.
Kit manufacturers have had to make these same types of decisions and in many cases the automotive engine seems to fit the bill in price, performance and respectable reliablity.
Do to the great differences in engine and kit models there really is no way to get too involved here on engine systems. Such subjects as engine mounts, cooling, lubrication, intake systems is too broad even for this website to handle. I can only give this bit of advise for those who want to construct their kit and get to flying it- stay with a powerplant selection recommended by the kit manufacturer. This will save you a lot of time.
I have two engine source pages for most engines commonly found on gyroplane kits. The certified and alternative engine pages will help you get in contact with engine manufacturers and repair parts or services.
A great engine reference for an automotive engine would be the fine manuals offered by the engine manufacturer. These are the kind your car dealership may use. These manuals can be very pricey. Another, cheaper option is to get the automotive repair manual for the vehicle in which the engine is installed. These manuals are available through Haynes and generally cost under fifty U.S. dollars. The engine section in the Haynes manuals will walk you through a complete tear down and build up. Haynes also prints these books in languages other than English. They can be contacted in North America at (805)498-6703. I also know Haynes has a publishing group in Somerset, England but I do not have a phone number for them.
Check out Cetificated Engines or Alternative Engines.