I'm just reading the book Advances in Elliptic Curve Cryptography, and Chapter II (by Dan Brown) is about provable security of ECDSA.
It lists some necessary conditions for the ECDSA components (group, conversion function, RNG, hash function), each with an associated forgery. For example, the group has to be resistant against discrete logarithms, as well as semi-logarithms.
With some additional conditions, we also get stronger unforgeability results, e.g. modeling the hash function as a random oracle means that semi-logarithm resistance also implies active existential unforgeability (i.e. the strongest result). Alternatively, modeling the group as an ideal group permits using only the necessary conditions on the hash function.
The book also contains sketches for the proofs.
Of course, this says nothing about whether a specific elliptic curve or class of curves really has the necessary semi-logarithm resistance, which seems to be what you really need.