A covenant is simply a binding agreement or treaty. A suzerain covenant is a covenant between a sovereign king (suzerain), in effect an emperor, and a vassal king and thus with the vassal nation. The terms of such covenants are decided by the suzerain king, they are not negotiated between the two kings. The suzerain covenant structures differ between empires and over the centuries.
One of main issues of discussion amongst archaeologists (not theologians) is not where suzerain covenants per se orginated, but which covenant forms the covenants of the Pentateuch are most similar to in structure.
The aim of finding a match between the suzerain covenant form of the Pentateuch and that of the ancient suzerain covenants is to put a date on the Pentateuch, the supposition being the author of the Pentateuch has used/copied the covenant form of the era in which he wrote.
So in the blue corner we have Professor Kenneth Kitchen with a lot about the different covenant forms over the centuries in the Ancient Near East (ANE). In the red corner we have Dr Bryant Wood.
Both take the Bible seriously, both believe the Exodus actually happened, and both argue that the Pentateuch was written before 1200 BC: both are emphatic that the Pentateuch could not have been written after this date, and the match of covenant structure in the Pentateuch with covenants before 1200 BC is yet another piece of strong evidence against a late writing of the books. This is what the evidence of the covenant forms from the Pentateuch compared to the covenant forms of the surrounding nations is telling them: and this is why the seeking of a match with the covenant forms of the surrounding nations is so valuable.
However, Kenneth Kitchen believes the Exodus happened about 1260 BC (Late Exodus) and Bryant Wood believes the Exodus happened 1446 BC (Early Exodus). And the date of the Exodus obviously affects the date of the writing of the books of and by Moses.
Kenneth Kitchen gives a large amount of information about the changes to the suzerain covenant forms of the surrounding nations (during the era of the empires of those nations, such as the Hittite Empire, when they were producing Suzerain/Vassal covenants) in his book "On the Reliability of the Old Testament". Since we know when those empires existed if we can see a distinct match between the Pentateuch covenants and those S/V covenants of other nations then a date can be placed on the writing of the Pentateuch. He then claims the best match of covenant puts the composition of the Pentateuch in the 13th century BC.
Bryant Wood claims that Professor Kitchen has been selective in his examination of the covenants in the Pentateuch and has resorted to a bit of special pleading. Bryant Wood also counterclaims that the existence of oaths in the covenants of the Pentateuch place them in the 1600 to 1400 BC period.
Unfortunately I cannot give an article by Kenneth Kitchen on the issue since my source is his book "On the Reliability of the Old Testament". Personally I think his date of the Exodus of about 1260 BC is wrong: he assumes that 1 Kings 6:1 is not to be taken literally, and this is a big mistake, in my opinion, but his book is still full of very valuable information for lovers of Scripture.
An article by Bryant Wood which touches on this subject can be found here:-