Realize at that point (June 1939) the RM had only the two reconstructed Cavours in service for capital ships. The two Dorias and first two Littorios won't be in service until 1940. So as I see it, sending capital ships is out of the question.
Similarly, with only seven heavy cruisers, with two squadrons of three plus Pola fitted as a fleet flagship, I don't think the RM can afford to give up any.
What the RM might be able to 'sell' to the KM that that latter needs are light forces. The early Condottieri cruisers, the Cadornas, don't have much range, and existing German CLs would be good for the Baltic. But the Montecuccoli class were more balanced, and have the best range of the Condottieri, so they might be usable as ocean raiders/escorts. Germany has a number of Torpedo Boats, but they are short of destroyers, so perhaps some of the Oriani or Soldati classes accompany a pair or two of light cruisers for the port visit.
The problem of course is, if Italy is going to get into the war, the Allies will have more numerous light forces than the RM, and the latter will need all the light forces it can get.
My thoughts,