There's quite a lengthy Facebook page about the entire park with several photos,
Golden Acre Park - The lost amusement park of Leeds. The grand opening of the Golden Acre amusement park was on the 29th March 1932, but the planning of the park began in 1926. This pleasure park...
www.facebook.com
The facebook page includes some showing the railway and its locos along with the following comment posted 5yrs ago.
The driver in the picture is Mr Henry Haigh. He is standing next to Robin Hood a 4-6-4 tank built by Hudswell Clarke of Leeds. Works number D570 ordered 11th september 1931 it left the factory on 21st March 1932. There was a later loco D582 of 30th May 1933 it cost at the time £1.480. Both are in fact diesel locos and both still exist. I last saw them in the museum at the Cleethorpes Coast Light Railway 2 years ago