15 x 10 tire suggestions

It’s the wheel opening I am concerned about @ 7/8”
The section width is your problem then (Assuming you don't have a full open wheelwell). The deal is: the wider the rim, the wider the tire needed.
You might have to go to a 255, but that is quite narrow for a ten inch rim.
The 275 (accord8ng to Tiresize.com) is 10.8", but that is probably measured on an 8/8 1/2 rim, section will be wider on your 10". Call it 11.1or 11.2, you will have a sidewall bulge toward your fender of about .6" .Very tight, might work.
What body style, and how high is the rear?