Reading a bit more about this, Peel Park and the Coppice were opened to the public in September 1909 HBC's website says:
On the Coppice there used to be four guns which were donated by William Peel in 1910. They overlooked Peel Park and Peel's Accrington House. This would tie in with the postcard picture's date of 1912 when the cannons would have been a relatively new attraction.
Oak Hill Park was opened in May 1893 and the Friends of Oakhill Park website says:
The mayor presented the two cannons which were installed in the higher position of the park now occupied by the War Memorial.
This suggests to me that the cannons in Oakhill Park are not the same as the ones on the Coppice although I can't be certain. I haven't been able to find any mention of what happened to the ones in the park.