Algorithm for checking unambiguity in the derivation of a string
gnasher's comment more or less answers this. A sketch of an algorithm would be: 


enumerate all derivations of the grammar that do not generate strings longer than $s$. This can be done, because CFGs do not have deleting rules (or if yours do, they can be converted for example to Chomsky Normal Form)
check how many of the strings generated are equal to $s$.


This takes a long time, of course. But I doubt that there is a fundamentally better way.