Theodore Roosevelt might be able to, but seeing as he's dead, no living Republican can beat de Blasio, even Giuliani.
Yes,
the man who came in third place in 1886 after a third party candidate running off of a gimmicky (and I'm saying that probably as his biggest fan on this forum) platform that appealed largely to radical Land Leaguers would certainly be the best bet.
All snark aside, New York City's politics have generally been pro-Democratic save for extreme circumstance. Looking at this
http://www.ourcampaigns.com/ContainerHistory.html?ContainerID=55648 it looks like that post-Civil War or so it looks like what has generally led to GOP rule is:
1. A VERY favorable environment for Republicans in general (I'm thinking probably the 1861 election, the candidates elected in 1894 and 1901 (generally very very good years to be a Republican) , Lindsay's election in 1965, and Giuliani-Bloomberg's first two terms).
2. Reactions against political corruption (this probably explains the on and off Republican victories during the late 1800s, Purroy's victory in 1913 (when the Democrats did very well elsewhere), LaGuardia's tenure (he even got FDR's endorsement). And even then a lot of the Republicans elected in these scenarios had a large amount of third party/dissenting Democratic help to do so.
From the looks of it third parties and independents have had just about as much success as Republicans have had running for Mayor of NYC. So yeah, if DiBlasio does go down it will likely be either in the Democratic Primary or because an ethics probe finds out he has been funnelling taxpayer money to fund his cocaine habits. And in the latter case it might be a tossup depending on how he spins it.