How to make a Java class that implements one interface with two generic types?

Because of type erasure you can't implement the same interface twice (with different type parameters).

Consider encapsulation:

public class TwoTypesConsumer {
    private TomatoConsumer tomatoConsumer = new TomatoConsumer();
    private AppleConsumer appleConsumer = new AppleConsumer();

    public void consume(Tomato t) { 
        tomatoConsumer.consume(t);
    }

    public void consume(Apple a) { 
        appleConsumer.consume(a);
    }

    public static class TomatoConsumer implements Consumer<Tomato> {
        public void consume(Tomato t) {  .....  }
    }

    public static class AppleConsumer implements Consumer<Apple> {
        public void consume(Apple a) {  .....  }
    }
}

If creating these static inner classes bothers you, you can use anonymous classes:

public class TwoTypesConsumer {
    private Consumer<Tomato> tomatoConsumer = new Consumer<Tomato>() {
        public void consume(Tomato t) {
        }
    };

    private Consumer<Apple> appleConsumer = new Consumer<Apple>() {
        public void consume(Apple a) {
        }
    };

    public void consume(Tomato t) {
        tomatoConsumer.consume(t);
    }

    public void consume(Apple a) {
        appleConsumer.consume(a);
    }
}