The G.I. jOE Green Beret was introduced in the Andy and George advertisements that appeared in comic books.

In 1966 Hasbro released the following Green Beret sets for the GI JOE Action Soldier:

 7528 Action Soldier Bazooka Set (carded; reissued 1967)

 - green camouflage bazooka and two bronze rocket projectiles.

 NOTE: In this set the bazooka is spring loaded to fire the rocket projectiles.

 7532 Action Soldier Special Forces Set (window box set)

 - green four cargo pocket jacket, green two cargo pocket pants, camouflage dickie, green camouflage  bazooka, two bronze rocket projectiles, four grey grenades and green beret with red flash insignia. 

 7533 Action Soldier Army Green Beret Set (carded; reissued 1967)

 - green wireless radio with headphones and key pad, black and brown M16 rifle, green beret with red flash insignia.

 7536 Action Soldier Green Beret (window box set)

 -  GI JOE action figure, green four cargo pocket jacket, green two cargo pocket pants, camouflage dickie, tan web belt, grey and black .45 pistol, black holster with orange leg tie down, four grey grenades, green wireless radio with headphones and key pad, black and brown M16 rifle and green beret with red flash insignia. 

 1969-70 Backyard Patrol Green Beret accessories

 The vintage 3dJoes site mentions the G.I.jOE Green Beret in just regular G.I. jOE Action Soldier green fatigues.

 I have seen loose G.I. jOE Action Soldiers wearing a green beret for sale on ebay from the USA, but just thought it was someone selling a regular G.I. jOE Action Soldier with a green beret, but it may be an exclusive Green Beret.