Here Oliver Cowdery initially wrote desireable in 𝓟, then virtually immediately corrected it to desireous by crossing out the able and supralinearly inserting ous (there is no change in the level of ink flow). The two words are, of course, orthographically similar and subject to confusion during copying. The context definitely supports the reading desirous since in English we expect desirable to refer to what people desire. Here king Limhi clearly does not intend to say that he himself is desirable. The critical text will maintain the corrected reading in 𝓟, desirous, especially given the immediacy of the correction.
Another example of possible confusion between these two words is in 1 Nephi 8:12. There scribe 3 of the original manuscript wrote desirus in the phrase “for I knew that it was desirous above all other fruit”. For the 1837 edition, Joseph Smith edited the desireous in 𝓟 to desireable, which makes better sense in modern English, although in earlier English desirous had the meaning ‘desirable’ (see the discussion under 1 Nephi 8:12; also see definition 5 under desirous in the Oxford English Dictionary).
Summary: Retain in Mosiah 8:12 the contextually appropriate desirous, Oliver Cowdery’s virtually immediate correction in 𝓟.