My $0.02 - before you pay someone to fill in your erosion issue, you may want to investigate what is causing the erosion. Is this a newer home? Is this going to be a recurring situation where you are bringing in 1-2 yards of dirt every other year? If so, talk with your builder about it. Is it a gutter issue - do you have gutters in the rear? If not, it would be wise to look into that additional expense and get that water away from the roof drip-line. Is there water coming from adjacent lots? If there is, is there any way to divert it away from the eroded area, i.e. re-grading away from the house foundation.
I've been disappointed in a lot of the home builders in the way yards are graded (or not in a lot of cases), but they will be the best people to know who can deliver and place the fill you need. Just make sure it's not a situation where you are having to do this over and over again after any substantial rain event.
And before anyone asks, I don't work for a contractor or gutter installer!