The only way I know to fix that problem is design the system so that sprinkler heads don't throw water over a sidewalk. That's against code in at least some areas, like mine.
If you don't want to tunnel the water supply under the sidewalk, might consider switching to Hunter MP rotator heads. They are the size of spray heads, and in fact you can use your existing spray head body and just buy MP nozzles. They put out multiple streams at a time, and rotate slowly, so are able to spray water further than spray heads. They also put water down much slower than spray heads, so you get less runoff. You can see them on Hunter's web site.