This old photo
For any process of applying color to a black-and-white photo or film, as in your first example, you could use the word "colorize" even if the process was not done by a computer.
I colorized this old photo.
Dictionary.com defines "colorize" as "to cause to appear in color; enhance with color, especially by computer"; "especially" implies that it is possible to colorize without a computer. Also, the Wikipedia article on film colorization has sections on both "hand colorization" and "digital colorization".
If you are dead-set on avoiding the word "colorize", then take Nathan Tuggy's advice and use the word "tint".
This coloring book
In your second example, you could use either "color" ["to give color to; to change the color of (as by dyeing, staining, or painting)"] or, as Tim Pederick suggested, "color in" ["to add color to (a shape or picture) by using markers, crayons, colored pencils, etc."]. The latter is more specific to coloring books, but both sound natural to my ear.
I intend to color this coloring book sometime today.
I intend to color in this coloring book sometime today.