Older Filofax personal organisers have plastic cover on the press stud on the clasp. Early Finsbury organisers had one, here's my A5 from about 2005:
Later ones like this Pocket had a leather cover over the press stud.
My elderly Winchester suffered from the plastic cover on the press stud cracking and eventually being lost completely.
Fortunately it left behind a metal dome, but I've seen ones where that too has been lost! I lived with mine like that for a while. But decided to smarten it up a bit.
So I already had some exterior grade black paint for use on metal work. I cleaned up the button with a little burnish and degreased it with a cloth and some white spirit. Then when it was all dry I dipped a cotton bud in to the paint and just let a small drop of paint flow over the button. Then I left it to dry in our warm office for a couple of days and here's the result.
Since the photo was taken I've given the leather a bit of leather care treatment and my dear olde Winchester looks as good as new again!
If you have lost the metal cap as well, then you have a couple of alternatives. You can either get a small piece of leather and stitch it over the exposed button. Or get the press stud replaced, this is best done by a shoe repair shop, you can buy the press studs from most craft shops or haberdashery shops. Or use a small bit of epoxy glue/putty to form a new cap and then paint this once the glue/putty has hardened.