No, the only rent allowed on the Homestead Property Tax Credit in Michigan would be property rented in Michigan.
It does not appear that Georgia offers a renter's credit.
Click the link for more details:
Filing Form 500, Nonresident tax return if you earned money in Georgia: 2019 Georgia Income Tax Book Instructions, beginning on page 12.
How do I file a nonresident return?
@anikawaddell
