I'm not sure if this is the kind of POD you want, but you could easily avert the OTL invasion of Albania by having Zog's wife, Queen Geraldine go into labour a day or so earlier than OTL.
Bernd Fischer, one of the major historians on 20th century of Albania posits that given Zog's concern over his wife and the continuation of his line, had Geraldine been in labour when Mussolini issued the ultimatum that preceded the Italian invasion Zog would have given in and accepted it. Accepting this ultimatum would satisfy the wording of the OP, but probably not the spirit as it would have greatly reduced Albanian autonomy and reduced it to little more than a satellite state. Zog would have likely been forced to declare war on the Allies alongside Italy during World War II and been offered Kosovo and Northern Epirus/Chameria as compensation. However, doing so would make it incredibly unlikely that the monarchy survives following the war.
As for turning Mussolini's attentions away from Albania, I find this highly unlikely given the folliwing:
A) Control of Albania had been an Italian strategic aim since the late 19th century
B) The sheer sunk costs the Italians had put into economically and politically colonizing the region
C) The international community's recognition of Albania as part of Italy's sphere of influence
and D) Mussolini's obsession with rectifying past Italian humiliations such as the defeat at the Battle of Vlora/Valona in 1920.
In short: Interwar Albania was in a really tough spot.
As for Albania restoring Zog, if he flees the country in 1939 as he did in OTL I find this incredibly unlikely. Zog succeeded in through equal parts selling the country to Italy and pursuing a strategy of "divide and rule" that left him tolerated but not loved. When combined with the corruption of his regime, the lack of development under his rule, and his antidemocratic actions these strategies made him incredibly unpopular. It is a testament to the failures of the Communist regime that Zog of all people is so highly thought of by some Albanians today.
Zog's son Leka, on the other hand is another matter. Most observers in the 1990s maintained that had Leka not shown up in post-communist Albania and acted like a complete thug/PR disaster he may very well have won the 1997 referendum to restore the Albanian monarchy.