a newly-married couple - We usually say "newlyweds" for this.
the just-married couple travelled to Scotland on their honey-moon. - We say "a recently married couple" not "a just married couple".
the recently-married couple decided to buy a new house over the beach. - This is okay, of course.
the freshly-married couples decided for sharing this area of the island. - No, "freshly" doesn't work here.
the latterly(lately)-married couple decided to adopt a 2-year-old boy. - No, this one is not good. Use this phrase: "the recently married couple".
Post any follow-up questions you have, but these are the phrases that we use for the things you want to say here.
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