No you can't do this.
Your account is associated with the region not the PS4 so even if you login to your friend's PS4 it will still ask for a payment method from the region of your account.
I'm assuming the problem is that you no longer have a valid payment method from your original region.
If you no longer have a way to pay from the same region as your PSN account there are a couple of things you can do.
Set up a new account on your PS4 for the new region and buy PS
Plus on this account. This is easy to do and you can still access PS
Plus features on your old account but you will loose access to any
free PS Plus games that are associated with your old account.
Buy PSN Gift cards from your original region online and use the
credit to buy the PS Plus subscription on you original account.