Early on he rode a Harley, then he started riding a Triumph, as I heard it, the Harley was too big[heavy] for him to handle.I should add, it was to big[heavy] to handle in the confines of the set.

Check Ebay for a 1954 Triump trophy Motorcycle. needs some rebuilding

Over the course of the series Fonzie posed with several different motorcycles. In the early episodes (cloth jacket) he was seen near a Harley-Davidson Panhead, Knucklehead, and a Sportster. In the later episodes (leather jacket) he was seen with Triumph 500cc and 650cc Triumph twins and once with a BSA. The bike most associated with “the Fonz” would be a mid-50’s to mid-60’s Triumph twin. A 50's Bonneville would work nicely and parts are readily available. Triumph also makes new bikes that greatly resemble the old bikes. In real life, actor Henry Winkler is terrified of motorcycles. During the 11 season run of the series there was only one scene of him actually riding a motorbike, a Triumph. He rode up a driveway and didn’t know how to stop the bike, crashing into two production assistants. (I read this in an interview with Henry Winkler from a few years ago.) Many of the 50’s bikes have the gear shift on the right and the brake on the left, opposite of today’s standard. If you learned to ride on modern bikes this can really throw you. I find it much easier to adjust to a foot clutch / hand shift (all pre-1952 Harley’s) than a right foot shift. Check the 1954 flick “The Wild One.” Marlon Brando’s bike is a 1950 Triumph Thunderbird and in one scene you can see him shifting into first gear with his right foot. (The Triumph he rode in the film was Marlon Brando's personal motorcycle.)