Oh yes I am familiar with gyros. Gyros like to precess. They need constant re-erection.
A gyro strong enough to keep that vehicle upright still needs to keep the center of gravity precisely above the center of vertical force. When the vehicle is stopped it has to be upright, but in a turn the force is tilted (which is why we lean in turns), so the vehicle will have to be tilted. To the gyro needs to allow such tilting, or the vehicle has to be driven so slowly that the lateral turning force is tiny.
My guess is a massive gyro with a vertical axis and the vehicle must be driven slowly.
I found this article:
Text of the article is below:
Designer: Alex Tremulis
In 1967, California-based Gyro Transport Systems hired the well-known designer Alex Tremulis to build a porotype car to be known as the Gyro-X. Tremulius - a famous stylist and Automobile Hall of Fame inductee - and Thomas Summers, a gyroscope expert, created the gyroscopically-stabilized prototype vehicles known as the Gyro-X. The result was the extraordinary vehicle with two wheels and a built-in gyroscope to keep it upright. It was powered by a transversely mounted 4-cylinder, 1275cc Austin Mini engine but the 'brain' of the car was a hydraulically driven gyroscope developed by the 'gyrodynamicist' Thomas O. Summers. Although technically a functioning success, the Gyro-X never went into production and this prototype is all that's left of the exercise. The vehicle was road tested by Science & Mechanics magazine, who wrote that it could reach a top speed of 125 mph and could sweep through turns without tipping, but the emphasis was on the word could for obvious reasons. Whilst warming up and before it achieved stability, a set of training wheels on retractable outriggers kept the car from toppling.
Proposed as a possible solution for future transportation, the two-wheeled vehicle provided many thought-provoking ideas for revolutionizing transportation. Why only two wheels? Tremulis and Summers suggested that a two-wheeled vehicle could be more efficient than its four-wheeled counterparts. Smaller and lighter weight means it can use a smaller engine. The Gyro-X was reported to reach speeds of 125 miles per hour using an 80 horsepower Mini Cooper S engine. Also, the gyroscope's stored kinetic energy would be harnessed as an additional power source in future gyro vehicles!
The aerodynamic body design reduced wind resistance, while half the number of tires reduced road drag. As far as drivability, two wheels made for greater maneuverability, like that of a motorcycle. While a two-wheeled automobile may at first glance seem unsafe and definitely unstable, the Gyro-X made use of a single 22-inch hydraulically-driven gyroscope which stabilized the vehicle, allowing it to 'swoop through 40-degree banked turns without tipping.'
The Lane Motor Museum acquired the car in running condition in 2012 and has recently restored it for the road. The restoration process has involved years of research and hard work to piece the car, and its history, back together.