Here are all the first-time NHL and NBA champions since 1967...
NHL:
1974 - Philadelphia Flyers
1980 - New York Islanders
1984 - Edmonton Oilers
1989 - Calgary Flames
1991 - Pittsburgh Penguins
1995 - New Jersey Devils
1996 - Colorado Avalanche
1999 - Dallas Stars
2004 - Tampa Bay Lightning
2006 - Carolina Hurricanes
2007 - Anaheim Ducks
2012 - Los Angeles Kings
2018 - Washington Capitals
2019 - St. Louis Blues
NBA:
1970 - New York Knicks
1971 - Milwaukee Bucks
1977 - Portland TrailBlazers
1978 - Washington Bullets
1979 - Seattle SuperSonics
1989 - Detroit Pistons
1991 - Chicago Bulls
1994 - Houston Rockets
1999 - San Antonio Spurs
2006 - Miami Heat
2011 - Dallas Mavericks
2016 - Cleveland Cavaliers
2019 - Toronto Raptors
So the only overlaps in the last 50+ years were in 1989, 1991, 1999, 2006, and 2019.
There are 11 teams in each league still seeking their first championship (excluding WHA and ABA titles). In order of senority:
NHL: Buffalo, Vancouver, Arizona, San Jose, Ottawa, Florida, Nashville, Winnipeg, Columbus, Minnesota, Vegas
NBA: Phoenix, LA Clippers, Utah, Brooklyn, Denver, Indiana, New Orleans, Orlando, Minnesota, Memphis, Charlotte