Hi Ian,
From all that I have been able to find, the Scott Bonnar Centenary was indeed named for the SA State Centenary in 1936. I have two of these and have had one running. They are very strong machines but the gearing is a bit quick. The knob on the side of the head is a decompression valve which is a common feature on Villiers engines of the time - Atco had decompression valves on the cylinder head for many of the larger engines until the 1930's. I believe these mowers were fitted with a variant of the Mk XI C (or XII C) Villiers - a 148cc engine that was introduced in 1931 and had a 53mm x 67mm. The Centenary mower appears to have been in production between 1936 and 1951. I am aware that Villiers were producing engines with fully covered flywheels as late as 1952.
I suspect that your machine, like mine, was produced post war from about 1949 - 1951.
Cheers,
Sir Chook
