I'm not sure if there is one already out there, but here are some issues to consider.
An engine has two main tasks: generating positions, and evaluating positions. It shouldn't be too hard in principle to create an engine that allows modifications to the rules and generates the positions; the search algorithm itself is pretty generic. The evaluation of the position is trickier since it tends to based on heuristics such as piece value, space, king safety, etc. which have been developed over the years for standard chess. The existing heuristics would likely be suboptimal for your variant, so you'd need to come up with them yourself if you don't want your engine to be too naive about strategy.
An engine such as Google AlphaZero doesn't need the heuristics because it can "discover" them by training, playing many times against itself. That would be an interesting way of implementing engines for chess variants, but I don't think it's readily available. Maybe some more lightweight machine-learning alternatives exist.
A caveat of traditional engines such as Stockfish is that they have been heavily optimized to save memory and time, and some of these optimizations might make drastic rule changes difficult. But if this is just for fun and research, a simpler, less optimized engine seems feasible and could be developed pretty quickly by a motivated programmer (shouldn't take years).