Single selects don’t have default values - so you won’t get that field pre-populated unfortunately. Your best alternative is using it in conjunction with a formula field (similar to what you’ve written).
But before I get to that, this part of your description is confusing:
if a new linked record “customer” has rent an item
Not sure how you’re using Customer (if it matters to the formula, what the data looks like when a customer rents an item). It’s tough to build an example without seeing your table. But ignoring the customer bit, you can do something like this:
Availability Controls (Single Select)
BLANK
Available
Rented
Availability Status (Formula)
Available
Available
Rented
Formula
IF({Availability Controls}=BLANK(),“Available”,{Availability Controls})
Formatted for Readability (this won’t run)
IF(
{Availability Controls}=BLANK(),
“Available”,
{Availability Controls}
)
Explained
If ‘Availability Controls’ is left blank, display “Available.” Otherwise just display whatever is in the ‘Availability Controls’ field.