There are 3 historic Saudi states - the 1st and 3rd Saudi States were particularly focused on conquests. The 1st Saudi State, from the early 18th century to the early 19th century, grew massively following the alliance of the Saudi emirs with Mohammad ibn Abdul Wahhab (the founder of Wahhabism). If I remember correctly, they did in fact attempt at least one invasion of Oman in the mid-late 18th century (Oman itself had just emerged from civil war and had a new and unstable regime), but the Omanis successfully retained their territorial integrity. I can't recall whether this is because of military victories or negotiations (the Wahhabis may not have been able to sustain their war into Oman).

Around 1818-19, Egypt sent an expedition against the Saudis (who had been threatening the pilgrimage to Mecca), defeated them, and razed their capital Diriya. The Saudis eventually reconquered and relocated to Riyadh and slowly recovered (this period, roughly from the 1820s to the end of the 19th century, is considered the 'Second Saudi State').

In the 20th century, under Ibn Saud, the Saudi emirs again began enlarging their territories through tribal alliances and conquests (most notably, the conquest of the Kingdom of Hejaz in the 1920s). By this time, however, territories of the Arabian Gulf littoral (including Kuwait, Bahrain, the 'Trucial States' - that is, modern UAE - and Oman) were under British control. The formality of each territory's relations with Britain differed, but by this point Ibn Saud could not touch any of these neighbours without bringing himself into conflict with Britain.