Relationships do not need conflict to be interesting. Think of Holmes and Watson, Nick and Nora, ET and Elliot, Roarke and Tattoo, Friday and Boss, Daneel and Giskard, Master Po and Caine, and so on, ad infinitum. Conflict and drama are fine, where appropriate, but forced conflict, and the inability to write an interesting relationship without conflict, is the crutch of the lazy or incompetent writer.
Relationships do not need conflict to be interesting--but
stories about relationships do.
Consider, for example, the relationships you list above--or at least, the ones I'm familiar with.
Yes, Holmes and Watson had an interesting relationship. But the stories in which they featured were not about that relationship. They were about solving crimes. The same is true for Nick and Nora Charles in
The Thin Man.
This was doubly true when it comes to Mr. Roarke and Tattoo. The stories on
Fantasy Island weren't about them. They were about the fantasies of people who visited the island.
Or, consider a relationship with which we should all be familiar: Captain Kirk, Mr. Spock, and Dr. McCoy. The stories in TOS were never really about their relationship as friends and colleagues--even though that relationship gave the series much of its lasting appeal. The stories in TOS were about how these three men resolved a variety of space-operatic crises.
Or, consider a movie I just watched this evening:
Invasion of the Body Snatchers. This movie actually sketched out a rather nice relationship between the main characters, Dr. Miles Bennell and Becky Driscoll: two divorced people who rekindle an old romance.
But this relationship is never more than a sketch, because the story is not about them rekindling their old romance. The story is about how their town is invaded by the body snatchers. Their relationship is mentioned solely to make them more rounded and sympathetic characters, and to make us care about them and their plight. And ultimately, to deepen the horror of the film's most horrifying scene.
If you're actually going to write a story
about relationships between people, then absolutely you need some kind of conflict. It doesn't have to be forced or melodramatic: in fact, ideally, it shouldn't be either of those things. The conflict, and the resulting drama, should develop naturally from character and circumstance.
But without some kind of obstacles to overcome, without successes and failures, without
drama, then what's the point of reading or watching?