In order to say two people as a couple, are perfect for each other, what phrases would you recommend to use as a complement? Something to express they are perfect match to each other.
A couple that "has good chemistry" gets along really well.
A "compatible" couple fit together really well.
A "power couple" are a couple that together, can do anything.
Edit for asker's visual:
A "cute" couple look good together.
A "good-looking" couple implies that the members of the couple are both independently attractive. (You could also use "hot", " sexy" or "attractive" and it would have a similar meaning.)
A couple that is "equally attractive" have a similar level of attraction. (Both members are attractive, or unattractive, etc.)
Whether two words, one, or hyphenated, one’s “soulmate ” is “a person with whom one has a strong affinity, shared values and tastes, and often a romantic bond: I married my soul mate; you don't get much luckier than that.” (from Dictionary[dot]com)
(Edited, not to steal @Elian’s good answer, but merely to point out the close connection between his answer and mine and that if his deserves down-voting, so does mine):
[The idea of soulmate is] more than about compatability … more than just being suited to each other. It’s as if you ‘belong with each other,’ and always have, and know it from the instant you meet.
(from ‘SoulMates’ via Google Books)
I would say, they belong with each other or they belong together.
We use belong with when we think something or someone is a part of a group, there is a match. For example, it would be very romantic to think that two people belong with each other. Two Min English
Do they belong together? Well, what other woman would keep taking back J.R.? Maybe Mandy Winger, doubtedly Cally, but Sue Ellen and J.R. have a history together. Remember J.R. let Mandy Winger go. I think he was more in lust with her though. Cally was another in lust situation. It's just that Sue Ellen knows what J.R. is all about. Mandy never knew the real J.R., only the loving one. Cally also knew about the real J.R., but she didn't go through hell like Sue Ellen did. J.R. and Sue Ellen were meant to be together. I would be surprised if there was a last and final Dallas that Sue Ellen and J.R. don't get back together again. I can see them getting married for a third time - as far fetched as that may sound. Anyway LOL to J.R. and Sue Ellen! Soap Chat
Going along with the visual aspect, consider they make a (very) nice couple.
Mr. And Mrs. Armstrong make a very nice couple and seem to be a perfect match for each other.