If you look at the gamemaker official tutorial for platformers, you'll see he has a basic staircase. This does similar to:
if place_free( to the left ) then move left
else if place_free ( to the left and up ) then move left and up
Using that sort of idea, it'd be fairly simple to make a loop of how much
up you're checking, and move to there (you'd probably want to make him move less if the slope is steeper).
For going down slopes, do the same thing. Just move it down instead. The character will cling to the slope, but it's better than moving to the side and then falling again and again.
EDIT: For obvious reasons, check for going down before checking for going up. Only move up if you can't go down...