Here are some dates that may be of interest:

1936 to Nov. 1949 - ROTS slogan on right side / SAW slogan on left side of UP boxcars.
Roman style lettering & slogans are initially white lead; slogans become Armour Yellow in late 1930s.

June 1939 - Gothic circle "O" style lettering starts on UP freight cars.
Lettering is white; slogans are Armour Yellow.

July 1947 - change lettering color to Armour Yellow on most UP freight cars (e.g. not tank cars).

Nov. 1949 to Nov. 1953 - ROTS slogan on right side / BSSUP slogan on left side of UP boxcars.
Lettering & slogans are Armour Yellow.

Dec. 1950 - spacing between two lines of BSSUP slogan increased to 18".

Nov. 1953 to 1961 - BSSUP slogan on both sides of UP boxcars.
Lettering & slogans are Armour Yellow.

Aug. 1956 - "Union Pacific" lettering changed from 10" circle "O" style Gothic to 20" oval "O" style Gothic on UP boxcars.


While I have no firm data, I would think that a generalized interval for freight car repainting would be hard to come by. Economic conditions (car use, labor availability - already busy painting new cars, money for paint), political conditions (wars, public image), management ideas (do they care if the cars are clean or dirty), etc. were not constant, yet all would affect freight car repaint intervals. It took a few years to repaint all the captive UP cabooses from red to yellow starting in 1947. Without shop records, photos are the next best evidence. And, what you are trying to determine is whether the lettering and slogan are the same color on each car. So even if dirty, we're comparing dirty white against dirty yellow.

Cheers,
Dick Harley
Laguna Beach, CA