They could place Maximilian de Beauharnais, duke of Leuchtenberg who is
A) married to a Romanov Grand Duchess
but also
B) Catholic,
C) not a "direct" Romanov, which makes it easier for other powers to accept the new situation, and
D) a member of the Napoleonic dynasty - and remember who just became President in 1848...this could go a long way towards fostering cooperation between Russia and France.
So basically an ideal candidate for the throne of a pro-Russian independent Hungary.