Couple things to consider:
Bolt head size. The 7.62x39 uses a smaller case head diameter than the 308 family. (.447 vs .473). It is easy to take a 308 barrel, cut of the chamber and re-chamber in 7,62x39, but the bolt head has to be modified.
As suggested, a 30BR is a small round that uses the 308 or BR family case and the 308 bolt head is just fine.
If you have an existing 7.62x39 rifle, then re-chambering to a Ackley Improved type round is your best bet. No mods to the rifle or barrel are required, except running a reamer into the chamber. One of the nice things about an Ackley is that it will still shoot standard ammo. The ejected brass becomes the new caliber case. If you are going to buy a reamer, JGS, for example, has a catalogue of standard reamers they make, which includs a number of "Improved" 7.62x39. These will shoot issue ammo and the larger case. If the design moves the shoulder forward, standard ammo won't work.
I used an old 308 match barrel and re-chambered it to 7.62x39 and installed it on a 788 action. Works well. With a 24X scope I use it as a test bed for testing milsurp ammo. It will put handloads with match bullets into less than an inch at 100. Milsurp runs 1.5" to 4"