Most applications specify that either an NRA instructor or the police can qualify you, but there is nothing in the law that says it has to be an NRA instructor. However, it's not really worth arguing with the licensing authority over that though..
There is a list of instructors here that might be able to help you out: http://www.rifol.org/forum/viewtopic.php?f=45&t=2524
If I remember correctly in RI you need to qualify with the caliber you intend to carry. In other words, if you qualify with a .38 you can only carry up to a .38. Most instructors I know in RI encourage their students to use a .45 for qualification.
Midstate will do your qual for you for $60 and I believe it includes the box of ammo....20rds of practice, 30rds for qual. Be sure to qualify with the largest cal you intend to carry, most do .45. 195 points or better out of a possible 300