None to my knowledge but it depends on what precisely you mean by 'rainforest building'.
Even as early as in the 19th c some European zoos began to built tropical greenhouses which hold, at least at some point in history, also animals. A good example is Antwerp's 600 m² Winter garden, a tropical green house which opened in 1897. To this day this building functions as a small rainforest, housing insects and butterflies.
Very few information & examples are available before world war II.
Large glass roof constructions were of course possible (the many botanical gardens are good examples) but for some reason no one built them to house animals.
In 1884 the Berlin Zoo opened its third Monkeyhouse, designed as a greenhouse with inside cages; in 1924 it changed in the Affenpalmenhaus. Still no real tropical rainforest, but this building got tropical plants as early as in 1884 (as seen on a picture in the Leipzig Illustrierte Zeitung in 1885 (source: "New Worls, New Animals. From Mengarie to Zoological Park in the Nineteenth Century", authors: R.J.Hoage and WIlliam A. Deiss).
In 1913 Zoo Berlin opened it's aquarium, a 3 story building with a crocodile hall which is at those days probably the closest example of a tropical rainforest : it has a glass top roof, a lush tropical vegetation and animals. The 1927 Wuppertal aquarium copied this style to house its American alligators.
So, in the first half of the 20th c I can't find any real tropical rainforest building. And even in the post war decades these buildings are almost non existing. Why?
However, technology is already available as early as the late fifties: in 1960 the Missouri Botanical Garden opens the Climatron Greenhouse, which was the first fully air-conditioned building made of plexiglass. Light materials and climate control systems are essential for large-scale tropical greenhouses.
So why are there so few tropical rainforest buildings in zoos. The given examples of the Capron Zoo and Topeka Zoo were unknown to me. Almost none are mentioned in the 'Construction and Design Manual. Zoo Buildings', (author: Natascha Meuser). Maybe there was no interest from the public?
The real stuff came in the eighties with Jungleworld (1985) and Burger's Bush (1988).
Even today, real rainforests building are rather rare in Europa (Burgers, Chester, Stuttgart, Beauvall, Vincennes and a few more) although many zoos have smaller facilities.