C#: Overriding return types

What about a generic base class?

public class Poo { }
public class RadioactivePoo : Poo { }

public class BaseAnimal<PooType> 
    where PooType : Poo, new() {
    PooType Excrement {
        get { return new PooType(); }
    }
}

public class Dog : BaseAnimal<Poo> { }
public class Cat : BaseAnimal<RadioactivePoo> { }

EDIT: A new solution, using extension methods and a marker interface…

public class Poo { }
public class RadioactivePoo : Poo { }

// just a marker interface, to get the poo type
public interface IPooProvider<PooType> { }

// Extension method to get the correct type of excrement
public static class IPooProviderExtension {
    public static PooType StronglyTypedExcrement<PooType>(
        this IPooProvider<PooType> iPooProvider) 
        where PooType : Poo {
        BaseAnimal animal = iPooProvider as BaseAnimal;
        if (null == animal) {
            throw new InvalidArgumentException("iPooProvider must be a BaseAnimal.");
        }
        return (PooType)animal.Excrement;
    }
}

public class BaseAnimal {
    public virtual Poo Excrement {
        get { return new Poo(); }
    }
}

public class Dog : BaseAnimal, IPooProvider<Poo> { }

public class Cat : BaseAnimal, IPooProvider<RadioactivePoo> {
    public override Poo Excrement {
        get { return new RadioactivePoo(); }
    }
}

class Program { 
    static void Main(string[] args) {
        Dog dog = new Dog();
        Poo dogPoo = dog.Excrement;

        Cat cat = new Cat();
        RadioactivePoo catPoo = cat.StronglyTypedExcrement();
    }
}

This way Dog and Cat both inherit from Animal (as remarked in the comments, my first solution did not preserve the inheritance).
It’s necessary to mark explicitly the classes with the marker interface, which is painful, but maybe this could give you some ideas…

SECOND EDIT @Svish: I modified the code to show explitly that the extension method is not enforcing in any way the fact that iPooProvider inherits from BaseAnimal. What do you mean by “even more strongly-typed”?