I need to change a participant to a co-owner

First step is to remove as a participant.

Remove a participant from your shared Apple Card account - Apple Support

Next step is to update both participant and owners iPhone

Update iOS on iPhone - Apple Support

Please do a forced restart of both iPhones

Force restart iPhone - Apple Support

Follow steps for inviting Family Member to co-owner

Invite an Apple Card Family participant or account co-owner

1. Open the Wallet app and tap your Apple Card.
2. Tap the More button , then tap Card Details .
3. Under People, tap Share My Card, then tap Continue.
4. Select a member of your Family Sharing group. To invite someone to join your Family Sharing group, tap Invite Someone.
5. To invite an account co-owner, tap Become Co-Owners.
6. Follow the instructions on your screen to provide the requested information.
7. Tap Send Invitation, then authenticate with your passcode.

On your iPad, open the Settings app > Wallet & Apple Pay > Apple Card > Info tab. Then follow these steps:

1. Under People, tap Share My Card, then tap Continue.
2. Select a member of your Family Sharing group. To invite someone to join your Family Sharing group, tap Invite Someone.
3. To invite an account co-owner, tap Become Co-Owners. To invite a participant, tap Add as Participant.
4. Follow the instructions on your screen to provide the requested information.
5. Tap Send Invitation, then authenticate with your passcode.

If you invite a participant who is under 18 years old, set up Apple Cash Family so that they can use their Daily Cash with Apple Cash. Some Apple Card users may need to contact an Apple Card Specialist in order to combine credit limits and form a co-owned account with another Apple Card owner. 

To accept invitation to become co-owner.

Accept an Apple Card invitation

1. On your iPhone, tap the invite notification or open the Wallet app, then tap the badge notification  in the upper-right corner.
2. Tap Continue.
3. If you're a participant, tap Accept Apple Card. If you're an account co-owner, follow the instructions on your screen to complete your Apple Card application. This includes a credit check.

On your iPad, tap the invite notification or open the Settings app > Wallet & Apple Pay. Under Pending Invitations, tap Apple Card to accept the invite.

To become an account co-owner, your application must be approved and you must accept your Apple Card offer.

Set up Apple Card Family and add a co-owner and participants - Apple Support