The above suggestion will only work if the part's edge is concentric. If the part's edge is a multiple-curved line (like a spline) then you aren't going to be able to array the feature in anyway. You'll have to individually constrain all the centers. Don't mistaken that as meaning you can't constrain all the centers in one sketch. If all the holes are the same size, then you can constrain multiple centers in one sketch and create the features in one command.
If the part's edge IS a single curve then: offset the edge the distance you need, make the line construction, define the first center. Use the circular array command but you'll have to know how many centers you want and the degrees in between each center.