Cadman kicked four goals in his first game of the season after returning from a pelvic injury to set up the Giants' comprehensive 20.11 (131) to 11.9 (75) victory in front of 10,508 fans at Barossa Park on Sunday.
But Cadman, 21, suffered a knee to the head in the fourth quarter and failed a concussion test, and Coniglio was ruled out before halftime after getting an accidental stray boot to the head from Sam Banks.
"He (Cadman) failed a HIA so unfortunately he'll miss Friday night's game against the Swans, which is disappointing," Giants coach Adam Kingsley told AAP.
"I thought he was fantastic for us - hard to play on, always on the move, launching at the ball, finishing his work - so (it's very) disappointing.
"Cogs is in the same boat, unfortunately, so we'll be without those two boys."
Kingsley said both were feeling OK and would work through concussion protocols and hope to face North Melbourne in a fortnight.
Cadman snagged three first-quarter majors in the Gather Round clash as the Giants piled on eight early goals.
"We re-established our scoring game, which was nice - we haven't been able to do that for three weeks," Kingsley said.
"I thought we started the game brilliantly.
"Our centre-bounce work and our stoppage work in general was awesome, so I was really happy with our performance."
Richmond fought back to within 20 points in the third quarter, but GWS kept the young Tigers at arm's length, then kicked away.
In their first game of the year after injury, Brent Daniels and Toby Bedford kicked three goals apiece, while Jesse Hogan nabbed two along with Ollie Hannaford, Ryan Angwin and Jake Riccardi.
With Nick Madden beating Tiger debutant Oliver Hayes-Brown in the ruck , Finn Callaghan (37 disposals), Toby Greene (29 disposals) and Jake Stringer were dynamic, and Clayton Oliver (31 disposals, eight clearances) was excellent.
Lachie Ash (35 disposals, 935 metres gained) was prolific and Jayden Laverde was strong down back.
Richmond's Mykelti Lefau kicked a career-best four goals and Liam Fawcett bagged three.
Sam Lalor (18 disposals, one goal) and ex-Giants Tim Taranto (25 disposals, 10 clearances) and Jacob Hopper (26 disposals, nine clearances) were busy.
"The response after quarter-time was a positive for the middle part of the game, but we just weren't up to standard for the first quarter," coach Adem Yze told AAP.
"To give up six goals from stoppage - one, that's not the right way to play, but it's not what you want to do on the road and at a different venue.
"Giving up that type of start, the alarm bells were ringing."
Winless Richmond next face North Melbourne on Sunday.
