Aloha David Here,
I have a pistol permit here on the big island and I am a resident here.
I am wondering if I could buy a rifle out of state from a dealer (me doing the 4473 in their shop and bringing it back here)? Who on the island does Dealer transfers?
Mahalo

I am a resident of another state. I go home a few times a year and buy guns (rifles, pistols, and shotguns). I legally have that gun shipped to me directly. I then register it in Hawaii upon arrival.

You may run into issues buying the gun out of states.... I think the out of state purchase varies by state.

If you travel to another state and purchase a long gun (and take possession at that time) you can bring it home with you on the plane or mail it to yourself.  I believe for pistols every state requires you to be a resident in order to purchase one.  When your rifle/shotgun arrives on Big Island you have five days to register it.  No FFL involvement is required for importing your already owned firearms.

Having a pistol permit does nothing for you.

If you order a gun online and have it shipped to Hawaii it needs to go through an FFL.  Are you closer to Hilo or Kona?  It's not hard to find one.  Gunbroker has an FFL search.