Is he trying to get this done cheap? the door sections were probably made out of some sort of pine, and if painted and not in an area where it stays wet all the time then pine will work fine for many more years (how old is the original door) you could jump up to cedar or redwood if you wanted more durability and longevity
If you go to an actual builders lumberyard you should be able to get #1 grade or very nice #2 2x6 lumber that if you pick through a bit you should be able to find boards knot free or almost knot free and very straight this could be ripped to your 4" and 1.75" rails and stiles i would guess that's your cheapest option
as another option, they should have or be able to get you 2x clear doug Fir but the price will jump
the same lumberyard should have or be able to get you 2x cedar or redwood but now you will start to get into decent money and might want to consider replacing the door with a steel unit (if its not an aesthetic issue to ditch the wood door)
you might also give a few local garage door companys a call and see what it would cost to buy wood replacement sections
John