To start off Kongzilla-thon, here is a compilation of the many attempts to bring Godzilla and King Kong back together on the big screen.
Continuation: King Kong vs Godzilla:
On August 11, 1962 and June 26, 1963, Japan and America would watch two iconic monsters fight on the big screen. Despite being a really goofy movie, King Kong vs Godzilla was the epic cross-over nobody would have expected and it was the ultimate "East vs. West" showdown at the time. King Kong vs Godzilla proved to be a big success in both the Japanese and international box-office and there were times where TOHO Co. would push for a sequel or a rematch.
Continuation: King Kong vs Godzilla was TOHO's first attempt at bringing Kong and Godzilla together again for a rematch. A draft of the script written by Shinichi Sekizawa was submitted in 1963, but ultimately the project never made it past the proposal stage. Godzilla would end up taking a break that year and TOHO Co. would move on to other projects.
Just as the movie's title suggests, Continuation: King Kong vs Godzilla would continue after the events of King Kong vs Godzilla. After Godzilla and King Kong fell into the ocean King Kong was the only one seen rising out of the water with Godzilla nowhere in sight.
After a plane crashes into the jungle of South Africa, a search party is formed to search for any survivors. They have discovered two things, only an infant survived the crash and King Kong has imprinted himself on to the infant. After rescuing the child, King Kong heads for Japan in search for the infant.
Meanwhile, Godzilla is dead and his corpse is being used as an attraction for a carnival attraction. With Kong on the rampage and the JSDF unable to stop him in his tracks, Japan is forced into choosing an ultimatum, give up the baby or revive Godzilla. Ultimately, the decision was made to revive Godzilla and force the two monsters into another confrontation.
What I have given you is the basic summary of the only draft made for the movie. Toho Kingdom has the full story of the script on their website. I suggest checking it out to those who are curious enough and have enough attention span to read the whole story.
Godzilla vs King Kong:
After Godzilla vs Biollante met with a mediocre performance in the box-office in 1989, TOHO Co. needed to make the next movie as profitable as possible. The only way to do so is to reintroduce one of Godzilla's older rivals from TOHO's roster. This ultimately led to them making Godzilla vs King Ghidorah, but one contender TOHO was eyeing on was King Kong. It would have made sense since King Kong vs Godzilla made such a large profit for the studio and remaking the movie would definitely draw in a large audience.
The story is mostly unknown, but in an interview with Shinji Nishikawa, he states that King Kong would have fell in love with a human scientist and would've had King Kong turn into a cyborg later in the movie. This would probably have meant that Godzilla would win the first round and devastatingly injured King Kong in the fight.
When TOHO Co. approached Universal Studios on the idea, Universal was in constant legal battles with companies such as Nintendo and Turner Entertainment over the rights to King Kong and his likeness. Universal offered TOHO Co. a very expensive number for the rights of King Kong, but TOHO Co. turned it down and decided to switch out King Kong for Mechani-Kong for Godzilla's Counterattack.