Not quite the easiest way to override Dagger 2 modules for unit tests...

ModuleOverride.java

@Component(modules=MyModule.class)
@ApplicationScope
public interface MyComponent {
    void inject(MyApplication application);
}

@Module
public class MyModule {
    
    @Provides @ApplicationScope
    public String provideString() {
        return "real string";
    }
}

public class MyApplication extends Application {

    @Inject public String injectedString;

    private MyComponent component;

    public void setComponent(MyComponent component) {
        this.component = component;
        component.inject(this);
        Log.d("Injected: " + injectedString);
    }

    @Override
    public void onCreate() {
        super.onCreate();

        if (component == null) {
            setComponent(DaggerMyComponent.create());
        }
    }
}

public class MyActivityTest {
    
    MyApplication app;

    @Before
    public void setUp() {
        app = (MyApplication) getInstrumentation().getTargetContext().getApplicationContext();

        // This is the sneaky bit. Create a partial mock of the Module you want to override,
        // then just mock the provider methods you want to override.
        MyModule module = Mockito.spy(new MyModule());
        Mockito.doReturn("mocked string").when(module).provideString();

        MyComponent component = DaggerMyComponent.builder()
                .myModule(module)
                .build();

        app.setComponent(component);
    }

    @Test
    public void mock_injected_successfully() {
        assertEquals("mocked string", app.injectedString);
    }
}

I've posted a new gist here using @tbroyer's idea: https://gist.github.com/vaughandroid/00287633102af6a66dc8