can friendly cup games be played on regional cup days or must they only be played on friendly days?

I got eliminated from my regional cup in only my second game so now have to wait 5 days between friendly dates and league games. it feels like such a loooooooooooong time. Looking to see if time can be filled with a friendly cup.

If it's possible who would set up cups as I don't think it can be just anyone.

freindly cups are played in lieu of friendlies not on cup days