I'm not sure how you could reduce the threat of aircraft... You could try treaties, but they didn't work very well in the 1930's. Japan ignored the Washington Treaty on naval construction, culminating in the 70,000 ton Yamato class battleships. Germany cast off the treaty of Versailles in a lot of ways in the mid 1930's, including the Bismarck class battleships.
The problem with those sorts of weapon limiting treaties is - the first nation to violate them has quite an advantage.
To realistically neutralize the effect of aircraft using 1950's technology, you might come up with effective anti-air missiles and guns, to make the battleship too dangerous for aircraft to approach. By the end of WW2, US warships had been so heavily armed with anti-air guns, many with radar activated proximity fuses, that only about one out of 15 kamikazes got through to actually hit a ship. That's an attrition rate far too harsh for pilots who need some expectation of survival to carry out their mission.
Had the battleship continued to be developed into the 1950's, possible future enhancements could have been longer range guns. The peak of battleship gun development were the 18 inch guns of the Yamato class, with about a 25 mile range. It is theoretically possible to equip a battleship with a single super gun whose barrel ran the 1000 foot length of the ship, that could have up to a 200 mile range. You'd probably need some sort of radar guidance in the shell to insure accuracy. However, that's not that big a leap over the radar proximity fuse, so it's feasible that a super gun equipped battleship might be able to hit an enemy fleet from 200 miles away, with the radar guided shell targeting an individual ship.
Won't they be surprised?
Improve the armor. Imagine a battleship made of titanium... would be horridly expensive to build, but you'd have either an extremely tough battleship, or a lighter battleship that had the same armor protection and a very high top speed. Or perhaps Chobham ceramic armor, as used on many main battle tanks today.
As an example of the benefits of high power and lighter weight, consider the liner SS United States. Built in the 1950's, it combined an aluminum superstructure for light weight, with a set of aircraft carrier engines, to yield a top speed of around 45 knots. (this was a 1000 foot long ship) This was done to give the US a very fast troop ship. That top speed was kept secret for decades... we didn't want the Soviets to know we could get troops to Europe a lot quicker than they expected.
The SSUS still exists, is tied up on a river in Philadelphia, while a group tries to preserve it as a museum. Sadly, that aluminum superstructure means it also has a fairly high scrap value, so its preservation is by no means assured.
Nuclear powered... would be a next logical step. High power, without the need to refuel. That could kick your titanium armored battleship up into the 60+ knot range. Try to hit that with a weapon powerful enough to get through the armor.
Underwater weapons, such as homing torpedoes, can be deceived. In WW2, the Germans developed the T5 homing torpedo, that homed in on propellor sounds. However, warships (who were the target of those torpedoes) could defeat that by dragging two parallel lengths of pipe (called a Foxer) behind the ship that simulated propellor noise, and the torpedo hit the pipes instead of the ship. While later torpedoes were developed with active sonar for guidance, that too can be spooked with decoys. As of today, the ability to defend a ship against attack has improved to the point where most major US warships are not heavily armored, relying upon the carrier battle group's defenses to stop threats before they can get through. (although the USS Cole was almost sunk by two guys in a zodiac, but that was more sloppy leadership in a potentially hostile port than anything)
Still, a primary reason the battleship became obsolete was not just its vulnerability to air attack, but the much greater range and accuracy of carrier aircraft. Perhaps you could develop such effective anti-air capabilities that a super gun on a battleship might be the only way to attack an adversary from a distance. That could justify the continuation of battleship design.