You can easily add your Copay wallet to BitPay by restoring your Copay wallet backup in the BitPay app.
If you have a wallet seed phrase (the twelve word backup phrase for your wallet), click the + under Bitcoin or Bitcoin Cash Wallet cards > Import Wallet > Wallet Recovery Phrase in the BitPay app and type your 12-word Copay backup.
If you've backed up your wallet in a file or text block, go to Add Wallet > Import Wallet > File/Text Backup in the BitPay app and upload your Copay text or file backup.
You will now be able to view the same wallet in both Copay and the BitPay app. Changes made to the wallet in one app will be reflected in the other.
To avoid duplicate notifications, disable notifications in one of your apps.
You can also delete a wallet from your Copay device (after you have imported it into BitPay) by clicking (in the Copay app) on the wallet Wallet > Settings > and selecting Delete Wallet.