https://www.tcdb.com/ViewCard.cfm/sid/11688/cid/571450/1999-Sports-Illustrated-Greats-of-the-Game---Cover-Collection-24C-Sparky-Lyle

https://www.tcdb.com/ViewCard.cfm/sid/5460/cid/1164384/1997-98-Score-109-Derek-Plante

https://www.tcdb.com/ViewCard.cfm/sid/255633/cid/15768836/2007-PAL-Pedigree-11-Brent-Harvey

If you consider fake wrestling entertainers athletes: 
https://www.tcdb.com/ViewCard.cfm/sid/67460/cid/5181658/2009-TriStar-TNA-Knockouts-49-ODB

https://www.tcdb.com/ViewCard.cfm/sid/224774/cid/14182213/1993-Bleachers-Nolan-Ryan-Promos-NNO-Nolan-Ryan-w/-Yellow-Lab-Puppy

https://www.tcdb.com/ViewCard.cfm/sid/54455/cid/599392/1992-Pacific-Nolan-Ryan-Texas-Express-II-120-Nolan-Ryan

https://www.tcdb.com/ViewCard.cfm/sid/298892/cid/17977906/1993-Pacific-Nolan-Ryan-Ghostwriter-120-Nolan-Ryan

https://www.tcdb.com/ViewCard.cfm/sid/56637/cid/596319/1993-Pacific-Texas-Express-120-Nolan-Loves-Animals

Nolan Ryan 2022 Stadium Club #23

Got one:

https://www.tcdb.com/ViewCard.cfm/sid/115847/cid/8683248/2016-Topps-450-David-Price

https://www.tcdb.com/ViewCard.cfm/sid/4908/cid/1199815/1992-93-Pinnacle-240-Uwe-Krupp?PageIndex=1

2018-19 Upper Deck - UD Canvas #C11 Johnny Gaudreau | Trading Card Database (tcdb.com)

2020-21 Upper Deck #191 Alex Ovechkin | Trading Card Database (tcdb.com)

1995-96 Upper Deck Be a Player #129 Curtis Leschyshyn | Trading Card Database (tcdb.com)

2015-16 Panini Complete - NBA Cares #21 Kyle Korver | Trading Card Database (tcdb.com) (Sort of)

C2Cigars - thanks for the help, that Sparky Lyle is great

donaldinho - Nolan Ryan sure loves his dogs! 

jdogg1228 - good find on the Price

SharksAttack - I would have never found that one

buckstorecards - added all of yours, debating on adding the Corver reading a dog book

I knew there were more, but I didn't expect this many.

Gotta add the Korver!

https://www.tcdb.com/ViewCard.cfm/sid/125069/cid/8424765/1988-WWF-Hostess-Wrestlemania-IV-Stickers-24-The-British-Bulldogs

1980s WWF’s top Four Legged dog, and valet for the British Bulldogs, Matilda

2019-20 Upper Deck - Day with the Cup #DC-9 Brayden Schenn | Trading Card Database (tcdb.com)

1993 Pro Line Portraits #471 Patrick Bates | Trading Card Database (tcdb.com)

2017-18 Upper Deck - Day With The Cup #DC8 Carter Rowney | Trading Card Database (tcdb.com)

2020-21 Skybox Metal Universe - Intimidation Nation #IN-26 Mikko Koskinen | Trading Card Database (tcdb.com) (He had his dog, Chili, painted on the side of his mask)

A few more for ya:

https://www.tcdb.com/ViewCard.cfm/sid/250421/cid/15520950/2020-21-Upper-Deck---UD-Canvas-C18-Kirby-Dach

https://www.tcdb.com/ViewCard.cfm/sid/62055/cid/3848936/1887-90-Old-Judge-(N172)-NNO-Arthur-Whitney

https://www.tcdb.com/ViewCard.cfm/sid/161337/cid/10753774/2017-18-Upper-Deck---Day-With-The-Cup-DC21-Phil-Kessel

Check out the 2017 Albuquerque Isotopes team set, pretty much every card has a dog

https://www.tcdb.com/ViewCard.cfm/sid/159839/cid/10512491/2017-Choice-Albuquerque-Isotopes-19-Ryan-Hanigan

Pretty much all her WWE-era card feature a doggie cameo

2021 Topps WWE Women's Division - Diamond Cuts #DC-8 Franky Monet | Trading Card Database (tcdb.com)

2021 Topps WWE Women's Division - Autographs Green #A-FM Franky Monet | Trading Card Database (tcdb.com)

A whole set of cards with dogs: 
https://www.tcdb.com/GallerySheets.cfm/sid/67622/1993-Milk-Bone-Super-Stars?PageIndex=1&Slots=9