Probably a dynastic marriage resulting in a union between the two countries, for which you'd need a way to (a) make such a marriage worthwhile (Abyssinia wasn't really that strategically important to the Romans) and (b) make their territories such that a union could work out (not much chance of that happening after the two became separated by thousands of miles of Muslim lands).
Maybe have the Byzantines keep hold of Egypt, but nevertheless be hard-pressed by the Arab invasions. As part of their defensive strategy they seek to form an alliance with Abyssinia, who can harass the Muslims in Arabia and the Red Sea and distract them from Roman land. To seal the alliance the two states conclude a dynastic marriage, then however many generations later the Abyssinian royal house dies out and the country passes to the Byzantine Emperor.