LOFL at Minnesota. The Twins won the championship in 1987 and 1991. The Vikings won the NFL championship in 1969. (And the Lynx have won 3 WNBA championships in since 2011.

) Minnesota is not in this conversation.
Buffalo won the NFL championship in 1964 and 1965. Plus, the Bills reached the Super Bowl 4 times and lost, and the Sabres reached the Stanley Cup finals twice and lost, so they got very close several times since 1965.
The Chargers have spent 52 seasons in San Diego with zero championships, and the Padres have spent 48 seasons in San Diego with zero championships. They also briefly had the Clippers and Rockets with no championships. The Chargers reached the Super Bowl 1 time and the Padres reached the World Series 2 times during that span.
Chargers "win" here, because they have the most total major sports seasons (110, counting this year for the Padres) without a championship, and, in fact, have never had a championship. The only other city that is close is Buffalo, and Buffalo teams reached the final game/series twice as often as San Diego teams, plus they actually won 2 championships in their history.