THESE Paint Brush pens are pretty good, my DD has loved these since tiny & still uses them now at 10yrs, you can get big multi coloured packs in toy stores & I think Argos too - they can't really damage the brushes in the way they do with felt tips & the coverage is much better than normal felt tips - if the brushes do get splayed from not putting away properly, just dip end in boiling water & reshape & let dry
my ds1 (13) and ds2 (10) have the staedtler and faber-castell pens, they are great, not cheap! BUT i wont let my little ones use them as they have been known to trash them, its berol for them or crayola for my toddler, esp as the crayola are more washable
Love the Faber-Castell ones but they are hideously expensive. They do last for ages and I have trusted DS to use mine since he was 6 or 7 without any nib crushing incidents. I buy them one at a time from Hobbycraft to split the cost. Not sure a 4 yr old would be allowed though. Maybe something to save up for in a few years because they are worth it.