U.S. Army Remington Carbine, .300.

Quarrel splashed out of the mangroves. He was carrying a rifle. He said apologetically. "No harm'n havin' anudder gun, cap'n. Looks like us may need hit."
Bond took it. It was a U.S. Army Remington Carbine, .300. These people certainly had the right equipment. He handed it back.

Dr No – Chapter 10.

As James Bond, Quarrel and Honey Rider head up the river to the former camp of the Audubon Society men, they are forced to hide from Dr No's men who are looking for them. One man is lingering behind, and Bond kills him. Quarrel takes the man's gun – a U.S. Army Remington Carbine, .300.

This was likely the M1 carbine, which was the standard firearm for the U.S. military during World War II, the Korean War and well into the Vietnam War. A lightweight, easy to use , .30 caliber (7.62 mm) semi-automatic carbine, this rifle was also very popular with military and police forces around the world. 

Dr No equipped his security team with them, showing, as Bond noted, that he gave his people the right equipment.