I also had problems with VPNs / errors when I signed up with Paramount Mexico (maybe it's a similar issuesto Argentina) - 8 months ago. The way I eventually got it to work was buying the 12 month subscription via the iTunes Mexico Store - it was a bit of a pain to do - i think i had to buy and send myself an iTunes MX voucher for 800 Pesos (and then the subscription via Apple was around 790 Pesos /£32 per year). I can't exactly remember how i did it, but I think I had to buy an MX iTunes voucher and then buy the Paramount subscription through iTunes. If you play around with it, you'll hopefully get it to work - sorry I can't be more help.
As an aside, I recently got an email from Paramount MX to say the annual price was going up to 979 Pesos (previously 789 pesos/year).
Paramount seems to have 2 apps / 2 subscriptions: (i) USA app - whcih only works with a US subscription (and VPN); (ii) International App - which seems to work in all / most other territories (if you turn on the VPN to whichever territory) i.e. you can use a Argentina log-in to watch Paramount+ UK provided your VPN is turned on to UK.