I agree with the above post.  There are several conflicts present in The Tempest because there are a few subplots within the course of the play.  All have to do with some type of sociopolitical hierarchy that the characters fall into during their lives.  As mentioned above, the main conflict revolves around Prospero attempting to get justice for having been usurped by his brother, but there are other conflicts as well such Stephano and Trinculo attempting to have a type of power that they would never be allowed anywhere else.  Similarly, Caliban is oppressed by Prospero who finds Caliban to be a base creature.  At the end of the play, many conflicts are resolved, yet it is unclear with Caliban's fate will be.  Ariel has been set free, but as far as the reader/viewer knows, Caliban is still Prospero's slave.

Of course, this question is purely subjective, and the answer depends entirely on what you see in the play. I disagree that the play contains no conflict. It perhaps may not follow the "norms" for what happens in Elizabethan/Jacobean drama, and many people think that the play was Shakespeare's farewell to the stage.  Still, the play is character-driven, mainly by Prospero, and it holds plenty of conflict. 

Prospero experiences conflict with nearly every other character in the play, from his daughter Miranda, who would love to get off the island, to Caliban, his unwilling servant, to Ariel, his willing servant, who yet wants to be freed from servitude. 

The story began with a long-ago conflict that caused Prospero to be banished with his daughter.  He is, at the time the play takes place, trying to bring a resolution to that old conflict, not just by settling a score, but by providing for Miranda's future.  True, things may work out fairly smoothly, but that does not mean that conflict does not exist in the play. It only means that Shakespeare was a master at dramatic resolution.

There is a conflict in the play.  It occurs within the character of Prospero.  One only has to look into the language to understand.  The man's mind is racing about.

He harbours a deep hatred of his usurping brother and those who helped him including the King of Naples.  He wants to get off the island.  He wants to find a suitable husband for Miranda.  It appears that he has been plotting his revenge for a long time and he has the power to do whatever he wants to his enemies once he brings them magically to his island.

His inner conflict of seeking revenge is resolved curiously by Ariel.  When Prospero asks about the condition of the King and his followers, Ariel explains their pitiful condition and tells the powerful magician that if he saw them he would feel pity.  When Prospero continues this line of questioning, Ariel tells him that if he were human, he would feel pity.

Prospero changes his mind because he realizes that, "Thought with their high wrongs I am struck to th' quick/Yet with my nobler reason 'gainst my fury/Do I take part.  The rarer action is/In virtue than in vengeance..."

Having written so many plays where violence and revenge lead to more bloodshed, Shakespeare chooses not to continue the violence in his final play.

Shakespeare's late plays are often criticized for various reasons because they do not conform to the established forms.  I contend that Shakespeare was experimenting with the late plays.  As a playwright, it was like, "been there, done that, how about if I try something different".  Like any genius, he was always looking for something new.