The station on the Kingston waterfront was known as Inner Station (the old CNR depot on Montreal Street was Outer Station). CPR 4-6-0 1095, on display next to Inner Station, most likely saw service on the K&P. My late father told me that he rode the Kick and Push from Harrowsmith into Kingston several times in the 1930s and 1940s, and that the mixed train consist he boarded was usually headed up by a CPR ten wheeler with a combine bringing up the rear.
When I visited family in the Kingston area in the 1970s, the southernmost 40 or so miles of the K&P, between Kingston and Tichborne, were still intact. By the 1980s, however, the last remnants of the line, as well as the old CNR line from Napanee up through Harrowsmith and Sydenham and on to Smiths Falls, were abandoned and removed.
As a note of historical interest, when Canada's first Prime Minister, Sir John A. MacDonald, died in Ottawa in June 1891, his body was transported back to his native Kingston on the Kingston and Pembroke. Thousands of people were on hand at the Inner Station on June 11 when the Old Chieftain who helped create the Canadian confederation came home for the final time.