Custom Error Handling for one module or controller

I have a module and I would like to set for it a specific action as the error handler action while keeping the error handler action defined in the main application. Is there a way to do that ?
I also tried to set it in the init method of a controller. It works in one application but not an other.

I would try to override the ErrorHandler::errorAction property. It can be done in Module::init method for example.