Here in Winnipeg there's a place called the Tire Exchange.

They fix leaks from driving over nails or screws by:
1. Taking the tire off the rim
2. Cleaning the tire on the inside around the hole
3. Putting a patch over the hole on the inside,
4. Using a special heater (called a Vulcanizer) to melt the patch over the hole on the inside of the tire.
5. Putting the tire back on the rim with a new stem and re-inflating.

They can do that work in about a half hour.

I would phone around to find out if anyone does those kind of repairs in your area. You should be able to find someone who patches from the inside with a vulcanizing machine.

If not, and if it wuz me, I would probably buy a repair kit for bicycle tires and use that. Have the tire taken off the rim and patch the sidewall from the inside with a bicycle tire inside patch. Still, if you can find a tire shop that installs patches from the inside, that'd be the way to go.

There's a lot of concern over the safety of driving on a repaired tire in this thread. To address those concerns, I'd rotate the repaired tire to the right rear position. That way, if you get a blow-out, it's not on a steering tire, and if you have front wheel drive, it's not on a traction tire either. Also, any blow-out you do get would cause the car to drift to the right instead of to the left into oncoming traffic.