Is this a 3 or 4 cyl.? If it is a 3 cyl., it should have an alternator, not a generator. Either way, any decent electrical shop can rebuild this for MUCH less than a new alternator or generator would cost.
Try the old battery post trick: With the tractor running, loosen and take off the positive side of the battery. If she keeps running, chances are that it ain't the charging system. If she quits, it probably is.