QGIS 2.12 has support for saving a layer on the map in the GeoPackage format and that is great. However, I don't see a way to add another layer to the GPKG file, even though GeoPackage supports multiple layers. Is this functionality that is yet to come in QGIS or is there a way to do it with QGIS 2.12?
DB Manager seems to have a bug working with geopackage data and can't be used to add another layer to a geopackage. You can use the 'save as' functionality in versions 2.18.1 and above. See: Add layer to existing geopackage not working in QGIS?.