Two easy steps:

Step 1

I used a RelativeLayout as parent of fragment with map and center in it an ImageView (which will do as the centered map marker just like in uber or easy taxi apps):

<!-- Map and ImageView in center for simulating the map marker -->
<RelativeLayout
    android:id="@+id/confirm_address_map_wrapper"
    android:layout_width="match_parent"
    android:layout_height="220dp">

    <fragment
        android:id="@+id/confirm_address_map_fragment"
        android:name="com.google.android.gms.maps.MapFragment"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        android:layout_centerInParent="true"
        />
    <!-- Image View that acts as map marker notice centerInParent-->

     <View
        android:id="@+id/view"
        android:layout_width="1dp"
        android:layout_height="1dp"
        android:layout_centerInParent="true"/>


    <ImageView
        android:id="@+id/confirm_address_map_custom_marker"
        android:layout_width="@dimen/ICON_DEFAULT_SIZE"
        android:layout_height="@dimen/ICON_DEFAULT_SIZE"
        android:layout_above="@+id/view"
        android:layout_centerHorizontal="true"
        android:src="https://stackoverflow.com/questions/19346206/@mipmap/my_map_marker"/>
</RelativeLayout>

Step 2

onMapReady() method at my activity I use googleMap instance method setOnCameraChangeListener() that lets me listen when the map is used and get latitude and longitude based on the center of camera position:

    @Override
    public void onMapReady(GoogleMap googleMap) {

        googleMap.setOnCameraChangeListener(new GoogleMap.OnCameraChangeListener() {
        @Override
        public void onCameraChange(CameraPosition cameraPosition) {

           Log.i("centerLat",cameraPosition.target.latitude);

           Log.i("centerLong",cameraPosition.target.longitude);
        }
    });

}

UPDATE:
OnCameraChangeListener is deprecated . Please use OnCameraIdleListener:
[Source: https://stackoverflow.com/a/38732283/421467]