In a 125-150gallon tank, I currently have 1 black tiger oscar, 1 albino tiger oscar, and a small shoal of silver dollars.

The non-albino oscar has suddenly become very aggressive and is actively chasing the albino oscar into hiding all the time. It even hunts it down when the albino oscar is hiding. Occasionally the black oscar would also try to take a bite out of the silver dollars, but they have been too quick for it.

I think my only option sadly is to give the black oscar away to a friend who can keep him if he keeps this up. In that situation, how many more fishes would I be able to stock in the aquarium now that theres only 1 albino oscar and a small shoal of silver dollars?

sounds like a wise decision.

How many silver dollars have you got at the moment? Don't forget that they can reach 6 inches so if you have three or four, that's quite a lot of fish. If you don't want to get another Oscar, you could go for a Severum or even a blue acara. However mixing cichlids is never straightforward especially if the empowerment is small. Many fish like living in groups so it can be difficult choosing just one fish that would be suitable.

there must be reason why one is hostile to other.
perhaps both are male that one want to establish
who is the boss. try to exchange with some one of
the same size to explore posibility of pair; male &
female.

i always want pair so that i can watch them dancing
gracefully as they grow most espacially the lip locking
rituals.

my previous two oscars were male and female and they were great! no aggression at all except when the female laid eggs. i guess both must be males =(

from my personal experience, albino oscars seem to be a little less aggressive. they seem to run more so then hold their own. the fish do have a slightly aggressive oscar, and as long as there is no real damage done, the albino will know when to back down. but if its real bad, youd have to bring the oscar back.

if you are to add another fish in exchange for the one oscar, id go with something they doesnt get quite as big as an oscar, something like a severum or a firemouth.