This is a bit of conflicting information on the two roller coasters at Bay Beach. In the "Bay Beach Amusement Park, a Pictorial History" from 1996 the following is written about the two roller coasters:
Cusick had built a roller coaster in 1901. It occupied the area where the softball diamond now stands. This roller coaster was torn down in 1922 due to insurance problems. Some of the Salvage was used as bleachers and backstops in some Green Bay Parks.
A second roller coaster known as the Grey Hound was approved by the park board on April 11, 1928, and remained standing until 1936. This coaster was erected by a private party known as the Green Bay Roller Coaster Corporation whose owner was Harry Broenig. The city received 15% of the coaster's gross earnings.
A park history page on the park's website on 9/24/2007 mentioned the following:
A roller coaster was built in 1901 and torn down and replaced in 1929. It was finally dismantled in 1936 due to insurance problems.
By 1910, Bay View Beach had become a favorite recreation spot. In 1911, Frank Murphy and Fred Rahr bought out Cusick and incorporated their park with Cusick as manager. Several rides were added including a large roller coaster and a merry-go-round.
The dates and information above is a best guess on the conflicting information.