There are tons of suitable engines and engine designs. The big problem is: Who would buy it? No manufacturer in the already niche, thin-margined, and overstocked business/charter jet market is going to be the first penguin off the iceberg to find that out. Even with a new subsonic model, one flop can mean a rapid financial death for the company.

There are plenty of other considerations outside of the factory floor and design rooms to consider - operating costs, the availability of qualified A&Ps to fix the thing, the parts network, the cost of the parts (if you buy a $15M plane, you're going to pay $15M plane prices for spares and overhauls). Insurance will surely take their pound of flesh for something that's A) a company's first product B) a new category, and C) supersonic. Finally, with the general public being decidedly anti-aviation, the noise profile of this plane might very well limit where it can fly in and out of. It's a basic matter of aeodynamics, and the same problem that the Concorde experienced almost 50 years ago.