You cannot get the Swiss Family Card if you (the parents) have not bought a Swiss Half Fare Card or a Swiss Travel Pass.
As you hold the Saver Day Pass, however, you can get the Junior Card instead. It costs CHF 30 per child, valid 1 year, and offers the same advantages as the Swiss Family Card: free travel when the parents hold a valid ticket. You can get the Junior Card from any SBB Travel Center in Switzerland.
Kindly note, the Saver Day Pass need your physical passports or any sort of official ID during ticket check to be valid.