My Italian informant Giorgio Briozzo tells me that we do not with any certainty know what flags the Swiss troops in Genoese service carried, which is very unfortunate. Stephen Manley in his booklet on the Flags of the Italian States in the WAS says that the Swiss Colonnella flags had the heraldry of Genoa on both sides and no madonna, as they were Protestant troops. He gives no references for that statement so I do not know how true it is.
So, in the absence of certain evidence, I decided to create some entirely fictional Genoese Swiss flags, just to please myself. I based them on Swiss flags carried by the troops of Naples and Modena. Here they are; please use or not as you wish! I think they look pretty good myself... :-)