Oman at the time was independent under Sultan ibn Ahmad Al Said and owned some African colonies and profited from the slave trade. All of this collapsed when the British decalred the trade illegal
Yemen had isolated areas under OE control at the time with much of the country under control of the Zaidi's. The Zaidi imamate collapsed and the OE moved in in the 1830's, controling San'a by the 1870's. Also in 1832 the British took Aden.
Here is a real interesting look at int
erior Arabia. To summarize the House of Saud and Wahhabists expanded greatly from 1744 to the point where they controled Mecca and Medina as of 1802. The Ottoman-Saudi War began in 1811 (presumably when Europe, or at least the Middle East, calmed down after Napoleon) and resulted in the recapture of the Hejaz and Nejd after some bumps. The Wahhabists and Sauds were treated brutally and their movement failed to die completley. A second Saud state and then the 3rd, saudi Arabia came about after this..
So it appears, Oman, Yemen, and al-Saud are all independent of the OE at the time. All would make good allies for the US as well...especially al-Saud in the twist of the centruy.