For a type-certified airplane (roughly "one built in a factory"), such an engine swap would require a Supplemental Type Certificate (STC). The process of creating such an STC would require a fairly extensive engineering study as well as flight-testing to prove the new engine was suitable in all regards. During that time period of developing the STC, you would place the aircraft into "Experimental" category to do the testing.

While possible, economically "it's not going to happen".

For non-type-certificated airplanes, there is a large grassroots community around "Experimental-Amateur Built" (E-AB) aircraft. EAA (www.eaa.org) is the largest owner club; they put on "Oshkosh" every year, which is the world's largest fly-in (of E-AB and factory aircraft). In E-AB, the constructor of the airplane has nearly full latitude to choose their engine setup (and to change it later). My limited experience suggests that those who start with tried-and-true aviation-origin engines have a higher success rate with their projects.