Mostly these displays use microwave doppler, similar to a police speed trap, laser time of flight could work too. Ultrasonic would be difficult over the required distance, it's also affected by wind.
Ultrasonic speed sensing can use doppler measurement similar to an ultrasonic burglar alarm. Unfortunately, the doppler shift at higher car speeds would exceed the bandwidth of usual sensors. A parabolic reflector could collimate the sensor wave to a small angle and achieve larger measurement distances.
P.S.: mikroepsilon has industrial laser time of flight sensors, but they are actually expensive. They are not designed for speed measuerements, but most likely fast enough to calculate speed from varying distance. Thess are basically point sensors, you possibly would want a wider angle of view for your sensor.
Said Parallax Ping sensors are specified for maximum 3 m operation distance :sad:
Parallax X band movement detectors specified for 9 m distance are operating based on doppler effect, but designed as a switch without a frequency output. Supplementing a similar device with a sensitive amplifier and a frequency detector, and possibly a reflector may work.