I came across an interesting article this morning. It has been released that crocodillians are able to climb trees. According to the article there are four species that can do so. They studied the different species in Australia, Africa and Nort America, but I did not see mention of which four species are able to climb trees.
I would not think that they could climb them very fast, but find this report to be rather interesting and would be more interested in knowing which species can do it.
Here is the link to one of the articles on this.