You can combine these sentences using either coordination to create a compound sentence or subordination to create a complex sentence.
Using Coordination to Combine the Sentences
A sentence with one independent clause (one subject-verb combination) is a simple sentence. You can combine two simple sentences to make a compound sentence, which is a sentence with more than one independent clause.
Coordination means that you make these two simple sentences into one compound sentence. You do this if you do not want one idea to be less than the other. The best coordinating conjunctions are and, but, for, nor, or, yet, and so. In this case, you could use the coordinating conjunction and to combine them.
The tabloids report that the King is just tired and wants privacy, and they give credit to unnamed reliable sources.
The best one to use if you are using coordination is but because the second sentence seems to discredit the first.
Using Subordination to Combine the Sentences
If you add an independent clause to one or more dependent (subordinate) clauses, you have a complex sentence. You make one sentence a dependent clause if the idea needs to rely on another idea. You can use a subordinating conjunction to do this.
The tabloids report that the King is just tired and wants privacy, however they give credit to unnamed reliable sources.
In this case, the word however serves much the same function as but in the compound sentence. The cluase beginning with however is the subordinate clause.