The kingdom of Sarawak, 500 000 pop., won by Sir Charles Vyner Brooke, later "white Raja of Sarawak"
"With little more than his 140-ton sloop and a bit of help from a British warship, he made himself Rajah of Sarawak, a kingdom of deep jungle and broad rivers on the island of Borneo."
And earlier it happened sometimes, when the kingdom mentioned was in the inner conflict. Such as Pisarro's conquest of Incs with 200 men.
"The term combat ...typically refers to armed conflict between military forces in warfare" So, single combat=single battle. And NOT a battle of singles.
If you really mean the personal fight, any case when a pretender killed a ruler personally and openly, fits for the question. And there were HEAPS of such cases in history of archaic "kingdoms"- power meant more, than the law. Or, rather, he, who has the power, sets the law. Of course, the pretender said that he is the lost son/nephew/grandson of the previous ruler, and if he did win, it WAS taken as the truth.
Don't forget, that there are other sources of power than army, too.
We don't need to go far ago - in Russia in 1999 it was Jeltsin, who had the army and was the president, but Putin made him to claim Pitin for the next president. Without even a single combat.