Presuming VEII isn't born posthumously (dunno when in '20 he was born) and Carlo Felice remains childless, then the throne of Sardinia goes to
http://it.wikipedia.org/wiki/Eugenio_Emanuele_di_Savoia-Villafranca in 1831, when he is only 15. AFAIK Eugenio Emanuele would be the ONLY Savoia left at that point until he had kids of his own. Now, he was morganatic until Carlo Alberto legitimised him OTL, but Carlo Felice will do the same thing if he wants his country to survive. CF's other option is to make his niece Maria Beatrice his heir, and unite Sardinia with Modena under a Habsburg offshoot. This is one step forwards, two steps back for Unification.
I have no idea how EE would affect Unification: all I know is that he was a military man who temporarily administrated Sardinia while his cousins were off gallivanting, and he married morganatically.