The first but in this passage seems inappropriate since we don’t expect the reversal in polarity implied by but; instead, we expect simply and (which is what the 1920 LDS edition emended the text to here in Ether 6:23). This desire of the people for a king was grievous, and therefore the brother of Jared told them that kingship would lead them into captivity. It is possible that the first but is an error caused by the following but (in verse 24: “but Jared said unto his brother”). Even so, there are examples in the original text of but being repeated within the same narrative (see the discussion under 3 Nephi 4:15–16).
Actually, what we have here in Ether 6:22–24 is a parenthetical clause, “and now behold this was grievious unto them”—that is, grievous unto Jared and his brother. (For discussion of the form grievious rather than the standard grievous, see under 1 Nephi 17:25.) The but of the following clause refers to the brother of Jared’s reaction to the people’s desire, not to his own grievousness. In other words, the text should be read as if it directly said “the people desired of them that they should anoint one of their sons to be a king over them but the brother of Jared said unto them”. The solution, then, is to separate off the intervening parenthetical clause with dashes or parentheses:
Under this interpretation, the sequence of two but ’s is perfectly acceptable. The first one refers to the brother of Jared’s attempt to reverse the people’s desire, the second one to Jared’s attempt to reverse his brother’s opposition to the people’s desire. Notice in particular that the them in the parenthetical clause (“this was grievious unto them”) refers to the brother of Jared and to Jared, while the preceding and following instances of them refer to the people (“a king over them” and “the brother of Jared said unto them”). By separating off the parenthetical clause, we also avoid any possible confusion over the referents for the various instances of the pronoun them. Thus the critical text will restore the original but in this passage.
Summary: Restore the original but in Ether 6:23 since the purpose of this conjunction refers to the brother of Jared’s attempt to reverse the people’s desire; this interpretation works if the intervening clause “and now behold this was grievious unto them” is treated parenthetically.