I suppose You have thought about interfaces and it doesn't fit for You - You need to inherit from two implementations, not interfaces. So the only way You can do that in Java is to use inner classes. It's not multiple inheritance, like in C++, but in most cases it should do. Inner class can manipulate the outer class object and each inner class can independently inherit from different implementation. Hope it helps.
Are you SURE that you can't use composition to get the benefits of inheritance? Couldn't your class just have an instance of one of the other classes and use that instance to get at its methods? Why don't you explain a bit about the classes and what you are trying to accomplish.