Early 'mark making' at age 2 is only going to be experimenting with crayons, paints or other materials, and a child's fine motor skills are unlikely to developed enough to produce anything anything recognisable, nor in realistic colours.
But that doesn't matter!! - the important thing for the child is CREATING something, that they can OWN and that gives them pleasure.
Dads are probably less sensitive than mothers to the hurt a child can feel if he doesn't 'measure up' to an adult's skills, which can sometimes make it difficult for a father and child to share activities together. Despite me being aware of these problems, I have occasionally upset our DS when he was little, by setting too high an expectation for him to meet, in academic or music activities. By age ten, however, he had outstripped me in virtually all areas!
A 'drawing' activity that, possibly, could be shared, is playing a game of 'BOXES'. A square grid of large dots is drawn by the adult, then adult and child take is in turns to draw a line to join two dots in a horizontal or vertical direction. The aim is to make as many 'boxes' as you can, and towards the end of the game, when you complete a 'box' you get an extra free go. Make the dots and spacing large, so a 2 yr old may have some hope of being able to join them. Each player has a different colour pencil.
When DS is doing his own 'drawing', don't quiz him on what things are; if he volunteers a description, OK, but DON'T EVER say it doesn't look like what he says, or suggest it is in the wrong colour. The 'ego' of a 2 yr old (or any child, for that matter) can be a VERY fragile thing.