1999 Volvo S80 will not hold a charge

Tricky ... Was the alternator replaced with a 2nd hand one or a new one?

A defective alternator can allow the battery to discharge within a few minutes (the diodes in the rear of the alternator can burn out and cause the problem. The diode pack can be replaced). When this happens recharging the battery only replaces the power in the battery - which drains straight back to earth via the alternator, flattening the battery again - often within a couple of minutes or less.

Does the battery lose its charge when the car is standing or just when the engine is fired up?
If the battery loses its charge overnight, try disconnecting the wiring from the rear of the alternator (also look at the electrical connector that fits into the back of the alternator - look for melting/burning marks which suggest something may be amiss inside the alternator).

Let the car stand overnight with the alternator wires disconnected. Will it start up ok and drive (with the alternator wires still disconnected) the next morning?

You could also try just disconnecting the alternator wires, firing up the car and then driving it -
If the car drives ok without dying out and gets further down the street than it usually does, then it probably is the alternator at fault. The car should drive until the battery drains and has insufficient power to trigger the ignition. You certainly would get further down the street with a charged battery and disconnected alternator than you currently do.

It does sound as though you've had an alternator fault to begin with. If it has been replaced with a 2nd hand unit that unit may also be faulty. Rather than replace parts in desperation, visit an auto electrician's - within a few minutes they will be able to test the battery/alternator output and also identify where the lost current is going. It will be cheaper in the long run to have an auto electrician look at the charging system. It only takes a few minutes.