A plot might involve a strange event that changes their relationship. Say, a magical force or an alien influence that makes them see each other in a different light. They start to communicate in a new way and gradually develop feelings. This could lead to a story full of challenges as they face opposition from other monsters or even humans who don't understand their new relationship. And it could also involve them learning about each other's cultures and ways of life, which deepens their bond.
Well, perhaps there could be a plot where they are both injured and have to rely on each other to survive. As they heal together, they start to notice the unique qualities in one another. Godzilla might be impressed by Muto's agility and Muto might be in awe of Godzilla's strength. This mutual admiration could turn into love. The story could then follow their journey of trying to make their relationship work in a world that doesn't expect them to be together, with them facing many external and internal obstacles.
One possible plot could be that they overcome their natural instincts as enemies. Maybe they find a common ground in protecting something in their shared environment, which then leads to a romantic connection. For example, they could both be trying to save a group of innocent creatures from a greater threat and in the process, fall in love.