Could you let me know the size of the tire and what brand is recommended.
Don't waste your money on a car tire. I tried a car tire on my Goldwing, it made it handle like a POS at low speed. After giving it an honest try(5000km) I dismounted it and put a motorcycle tire on.
How well do you follow regular maintenance? If you're good about it, the car has developed a unique problem and needs to be diagnosed by an experienced friend or professional. If you just drive the car and never take care of it, it could just simply be overdue for a fluid change. NOTE: A transmission flush is almost never a good idea. There is plenty of proof on this subject regarding damage to transmissions AND service bulletins from various manufacturers (including Honda) stating that transmission flushes are unnecessary services for their vehicles.
You really don't want to install any car tire as most expect for skinny spare tires are usually too flat on the tread and that will interfere with the handling in the corners.
Depends some on tire and purpose- the sidecars users have put car tires on the cycle rims or a custom rim with compatable bead seat. Suzi has some models with 15 inch rear wheels, the old VW tire was used on some of the sidecar rigs. A few 2 wheel rigs have used a rear car tire- mostly drag strips, sometimes a snow tire for off road racing. A few people have put radial Pirelli car tires on heavy cruisers for mostly straight line highway use, going for longer tire life, they accept the slightly poorer handling in tight curves but rarley push a fully loaded dresser in corners.
It could be a simple sensor that needs replacing. Take to a Mechanic to have it scanned.