Edit with new rulers:
-Guido Ascanio Sforza di Santa Fiora (Sede Vacante) (1549-1550)
Coin example: N#331974
Later Sede Vacante years by him are already on Numista
-Ludovico Trevisan (Sede Vacante) (1464)
Coin example: N#331977
-Benedict XIII (1394-1423) (Anti-Pope)
Coin example: N#337981
Urban VI (1378-1389)
Coin example: N#338432
-Clement VII (1378-1394) (Anti-Pope)
Coin example: N#278894
-Innocent VI (1352-1362)
Coin example: N#300485
-Clement VI (1342-1352)
Coin example: N#339426
-Benedict XII (1334-1342)
Coin example: N#300487
-John XXII (1316-1334)
Coin example: N#278893
-Pietro di Montebruno (Sede Vacante) (1268-1271)
Coin example: N#339792
It seems like some are during some phase of a Roman Senate? I'm not that familiar with that part of history. But I guess it should be possible to give these coins a clear ruling authority.
Also, it seems like not all of these should be listed under the Papal States to begin with (I guess it makes sense for Anti-Popes at least).