Simple: Someone posts a prime minister, and someone else adds another to the timeline and it goes on until we start a new one. I'll start.

James Garfield Gardiner (LIB) 1946
 
James Garfield Gardiner (LIB) 1946
Lester B Pearson (LIB) 1951
Norman Manley (Labour) 1955

(I'm adding a detail that this Canada is a different nation because Britain passed off its Caribbean colonies to Canada at some point, probably in the 1920s. Feel free to ignore if this is a problem.)
 
James Garfield Gardiner (LIB) 1946
Lester B Pearson (LIB) 1951
Norman Manley (Labour) 1955
Tommy Douglas (Labour-CCF) 1961
 
James Garfield Gardiner (LIB) 1946
Lester B Pearson (LIB) 1951
Norman Manley (Labour) 1955
Tommy Douglas (Labour-CCF) 1961
Donald Fleming (Liberal Conservative Party) 1965

The Liberal Conservative Party was founded similar to the Progressive Conservatives OTL as a business oriented coalition to combat the NDP and Labour parties, bringing many Blue Liberals in as well. Think of the Liberals in BC. (If anyone has any ideas for OTL Liberals on the right wing of the party for any era they would be good to use as well.)
 
James Garfield Gardiner (LIB) 1946
Lester B Pearson (LIB) 1951
Norman Manley (Labour) 1955
Tommy Douglas (Labour-CCF) 1961
Donald Fleming (Liberal Conservative Party) 1965

Robert Stanfield (Liberal Conservative Party) 1972
 
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