Carving a path from the Hudson Valley to the Balkans requires patience, since no carrier offers a one-stop shortcut worth bragging about — but the routing possibilities more than compensate for the extra connection. There is no nonstop business class from Albany to Belgrade, so the practical answer for most travelers is a positioning flight out of Albany to a major East Coast or European gateway, followed by a long-haul business class segment on Lufthansa, Turkish Airlines, or Air Serbia (JU), the last of which operates the only true single-carrier link into Belgrade's Nikola Tesla Airport. My preferred routing funnels through Frankfurt or Munich on Lufthansa, where Allegris business class has started appearing on select long-haul aircraft, offering suite-style seating with a sliding door on the newest configurations — though on this itinerary you'll more often encounter the reliable, fully-flat Business Class seat on older 747-8s and A350s, still a comfortable way to cross the Atlantic.
Turkish Airlines via Istanbul is the wildcard worth considering, particularly for the food-obsessed traveler: the airline's Business Class catering, complete with an onboard chef service on widebody aircraft, remains one of the more theatrical dining experiences in the sky, and Istanbul Airport's Turkish Airlines Lounge is worth the layover time on its own merits. If schedules allow, I've found connecting through Munich rather than Frankfurt shaves real minutes off tight layovers, since Lufthansa's Munich hub has shorter walking distances between international arrivals and the Star Alliance transfer security line — a detail seasoned Star Alliance flyers rarely advertise.
January through March and again in October and November consistently produce the softest fares on this corridor, largely because Belgrade sees its heaviest leisure demand in summer. Business travelers heading to Serbia's growing tech and finance sectors tend to book late, which pushes premium inventory open during shoulder season. Given how thin premium cabin allotments are on this route, setting up fare alerts is genuinely the smartest move you can make before committing to a booking.
