Another way is through character backstories. If the fanfiction delves into their pasts, perhaps they find out that they have some sort of connection from long ago. This connection can be explored and can bring them closer together. For instance, they might discover that their families were once allies, and this realization makes them see each other in a new light.
One idea could be that Inuyasha and Kirara have to team up to protect a special magical item from a powerful demon. Along the way, they discover new abilities in each other and form a deep bond of friendship that might turn into something more.