The most direct way to keep the Savoy in tge spanish throne is probably to keep General Prim alive. In OTL he was murdered soon before the arrival of Amadeo, depriving the new king of his main and most powerfull protector, and also the mastermind behind the proclamation of Amadeo as king.
General Prim i Prats is one of the most interesting figures in 19th century Spain. Born in the catalan middle class, hero in the first spanish-moroccan war after he led personally the charge of the catalan legion (catalan volunteers) against fortified moroccan positions, breaking the enemmy line (nowadays, the Palace of the Cortes is "protected" by two bronze lions made with the cannons captured that day) and a man with contacts in the high levels and the sympathies of the common people. He was also a convinced democrat and a capital fgure in the Progressive Party and of course took part in the overthrown of the Bourbons in 1868. He supported Amadeo in order to give stability to his designed liberal constitutional monarchy. He had brain, guts and principles, a rarity in politics. Unfortunatelly he wasn't republican, but that's only my personal opinion.
He had been also in duty in Cuba, where he stablished somewhat cordial relations with the cuban nationalists and supported a sort of dominion status for Cuba and Puerto Rico.
So, with Prim caring behind the scene, or over it, there are so many posible POD's that I don't know where to start....
EDIT: I mean, this guy: