Salome
Alexander didn't
mint in her own name, though the
overstruck coinage of
Hyrcanus II was surely struck by her in her son's name, as it only makes sense as an issue produced in haste after Jannaeus' death. Salome, of course, was not High Priest, and while the title 'king' isn't always used or claimed, 'High Priest' is, so presumably this was the vital thing at the time. Aristobulus ruled for four turbulent years, while most of
his family ruled for considerably longer, and all the evidence I've seen suggests that minting in Judea was intermittent, with bronze being produced as needed. It may be thet he just didn't need to produce any coin during that relatively short period, or maybe there was a shortage of metal, as there appears to have been at one stage under
his father. Or, alternatively, the coins might be out there somewhere, and we either just haven't found them or we haven't attributed them correctly yet!
Hendin discusses one interesting possibility, that the
overstruck coins of
Hyrcanus II could in fact be coins of
Jannaeus, restruck after
his civil war with the Pharisees with the abbreviated form of
his name, Yonatan rather than Yehonatan (which is used in reference to him from the Dead Sea Scrolls) in order to avoid using the letters YHO, which is also used as an abbreviation for the Divine Name. Such usage would have been offensive to the Pharisees. If this is correct, then neither of
his sons minted coin as far as we know. However, given that
Jannaeus is said to have crucified 800 of
his political opponents, probably mostly Pharisees, at the end of the civil war, he's hardly likely to have made such a concession to their sensibilites.
His widow, however, supported them, so it would make sense for the abbreviated form to appear on any coin she struck.
I think my 'best guess' would be that so much coin was struck under Aristobulus' predecessors that there was an ample supply, and
his brief reign being so turbulent, he probably
had other priorities.