The Yankees, instead of using a bullpen cart, used a pinstriped Datsun, provided by the automaker, one of the team's sponsors, then in 1976 and 77, used a Toyota Celica

https://boards.sportslogos.net/topic/89911-bullpen-carts

https://chicago.suntimes.com/2018/3/6/18348801/bullpen-cart-makes-its-triumphant-return-thanks-to-arizona-diamondbacks

https://www.ebay.com/itm/312852682687

In 1979 you could buy the #Yankees pinstriped bullpen car out of their catalog, only $8,349.75!

https://www.mlb.com/cut4/the-history-and-mysteries-of-the-mlb-bullpen-cart-c210932342

then a Dodge Aries

in 1951 the Yankees used a black hearse from a nearby funeral home.

Harley, in 1959, used a Topper scooter

St. Louis Cardinals pitcher Hal Jeffcoat, brought into the game to replace injured starter Alex Kellner, by County Stadium's new bullpen cart, driven by Harley's John "Freckles" Bonneau, complete with chauffeur's uniform and cap — as the pitcher exited the vehicle and went to the pitcher's mound.

Milwaukee finally got classy though, The last bullpen car in the big leagues was actually a Harley-Davidson motorcycle with a sidecar that the Milwaukee Brewers used in 1995

https://blogs.fangraphs.com/the-idle-thoughts-of-the-first-pitcher-to-ride-a-bullpen-cart-in-2018/

https://www.northjersey.com/story/sports/mlb/yankees/2018/03/14/would-new-york-ny-yankees-relievers-ride-retro-bullpen-cart-least-d-rob-yes/426408002/

https://www.nytimes.com/2012/10/12/automobiles/a-baseball-veteran-returns-to-the-mound-the-bullpen-car.html