I'll give it a shot
Unfortunately my knowledge of the subject is limited so I'm going to have to rely on a "Great Man" POD. This man, let's call him Giovanni, is the perfect man for Trieste. He was born in 1910 and in OTL he was inadvertantly killed in a terrorist attack in the region. However in TTL he survives the attack and goes on to change the world.
The son of an Italian father and a Croat/Slovene mother Giovanni grows up in a very multicultural environment. Never a fan of Mussolini, Giovanni goes on to become the editor of an anti-government newspaper, printed in not only Italian, but Croatian, and Slovenian aswell. This makes him very unpopular with the Italian Fascist regime prompting him to go into hiding prior to WWII.
During WWII, Giovanni joins up with a local anti-fascist resistance group known as TIGR and quickly rises through the ranks due to his charisma and military skill. Upon the event of Italy's surrender Giovanni's influence sees TIGR grow immensely as Italians begin joining in large numbers and in addition large numbers of Italian arms are acquired by the group before German and Croatian forces move in. TIGR later plays an important part in the liberation of the area working with both the armies of New Zealand and the Yugoslavian Army.
Post-war sees Giovanni and numerous ex-TIGR members grow quite popular in the region working with the local governing authorities to establish and maintain order. Giovanni's old paper is restarted and begins widespread circulation in the Free Territory of Trieste. In the 1939 elections Giovanni, cooperating with his old TIGR comrades founds the Democratic Coalition party the only other polyethnic party besides the Communist party. Giovanni's popularity, his centrist views, his heritage, and an amazing campaign lead to him winning a majority of the seats in the election.
Under Giovanni a constitution is written for the country and numerous reforms are enacted as the region travels down the road to independence. In 1955 the Free Republic of Trieste is established with conditions much like Austria (everlasting neutrality written into the constitution.)
Neutrality in the Cold war sees Trieste participate in the Western European miracle due to Marshall plan aid. And though the initial years were shaky, Giovanni's superb leadership sees Trieste develop into a "model multi-ethnic state". 1970 sees Giovanni turn 60 years old, having lead the Democratic Coalition party and by extension Trieste since it's inception the aging leader begins preparing for his retirement. Giovanni retires in 1973 leaving the 1974 election to his successor Ivan Radjik a Slovenian fluent in both Croatian and Italian. 1974 sees the DC party split between the Conservatives and the Liberal wings. However both parties remain multi-national and 1974 sees Ivan Radjik lead the Conservative party to a narrow victory ensuring the stability of the tiny nation.
Trieste's military always astounded many. Following a state visit to Switzerland, Giovanni instituted a similiar system in Trieste forming a Triestian National Guard. Said national guard tied the country together in a large way and would later participate in a number of UN peacekeeping missions. In addition crime rates dropped to an all time low as every eligible male was required to join the guard.
The death of Joseph Broz or Tito and the end of the cold war however would put the Free Republic of Trieste to the test as the entire nation of Yugoslavia collapses hurtling the tiny republic into a whole new world.