There are two choices I know of. I had this problem on my 64 FHC and found a cotter key wedged in my oil pressure relief valve. The relief valve is on the oil filter assembly. So check there first.
The only other thing I know of is main bearing going which will require a lower end overhaul.

Mine had this problem when I paid $1000 for it in 1974. When I test drove it I watched the oil pressure drop from 40 PSI to 0, but it was strange to me that the engine was not making any metal or knocking noises. So I took a chance on it. When I took the relief valve apart and removed the cotter key (no clue where it came from) I drove the car for another 10 years without a problem. Then I decided to rebuild for some reason but no oil pressure

So check you relief valve