The small "D" frame Colt's use a stock pin specific to them.
These are smaller then medium "E&I" frame models like the Python.

The frame pins are very often really tight fits.

The pin can go in from either side, but a sort of standard on firearms pins is usually to install from the right side.
This is not always the case and the Colt frame pin isn't side specific.

Options.......

Put the pin end in a drill, run it at medium speed and use wet or dry fine sand cloth over something like a file to SLIGHTLY reduce the diameter so it's easier to install.

Better option is to use a vise as a press to install the pin, which does need to be a tight fit in the frame.
Get a buddy to help hold the gun to prevent slipping and damaging it.
Put a block of some sort with a hole to pass the pin in one side of the vise.
Put brass or copper sheet in the other jaw to protect the pin.
Position the pin into the frame hole with the frame in the vise.
Tighten the vise to press the pin in.