There are really only three ways that I know that allow one to definitively arrive at a date for any text. The first strategy: one can determine the terminus post quem (time after which) by establishing the last independently-datable event to which the text refers, and the terminus ante quem (time before which) be looking at its first attestation in external evidence, such as manuscripts or quotations. This typically yields a range of dates, and thus often constitutes just an initial framing of the investigation; usually one or both of the other two strategies will be necessary to arrive at a date within the identified range. The second strategy: one can look at references in the text to the time of the author: the author might say "In X year of Y king I write this book." Or she or he might mention an event occurring at that time. Then we can synchronize that statement with chronologies known on other bases. Third strategy: one can consider accounts of the text's origin or the author's life in other texts.
The problems come when we consider the nature of the data. With most of the NT, the first strategy yields a range from the mid-first to mid-second century C.E. Narrowing down to a century or so is a good start, but only a start. The second strategy is of but limited use to us. What little use we can make of this strategy requires synchronization with the data provided by the Acts narrative, Josephus, Tacitus, etc., and is largely limited to certain Pauline texts and probably also Revelation. The third strategy is in fact where we find the majority of our data. We have a wealth of second century material discussing the origins especially of the gospels, the lives of the attributed authors, etc. Operating on the dictum that the scholar should go where the data lives, this is where the historian interested in the origins of the New Testament texts should be spending the bulk of her or his time. Strangely, it is where such historians tend to spend the least.
This, I suggest, is why we tend towards great imprecision in our historical narratives. We'll say that, for instance, Luke's Gospel was written in the 80s. By whom? Shrug. Where? Shrug. The thing is, our shrugs are not necessarily due to the state of the data, but rather because we have conscientiously refused to consider a large amount of data in developing our reconstruction. One of course cannot simply take these data at face value (anyone who would object to using such data on such a basis obviously does not actually understand the role of data in historical investigation), but neither can one operate as if they do not exist. If one does, one should not be surprised if one is unable to find answers. It's hard enough to assemble a puzzle; when one throws out two-thirds of the pieces it becomes virtually impossible.