The problem with your question is that it seems based on a misunderstanding of what Greek myths were. Greek myths come to us as a body of classical literature that codified stories circulating in contemporary oral tradition. Ancient Greek writers were doing something similar to what the Brothers Grimm did in the nineteenth century, namely, writing down stories that they heard. There were of course huge differences, chief among which was a tendency among ancient writers to attempt to iron out contradictions that are a natural aspect of oral tradition.

We could talk about the last of the Greek writers to have written, inspired by this body of oral tradition, but I don't think that's what you're asking (although I'm not sure). We cannot answer questions about what is the oldest or the youngest Greek myth, because the body of literature that depicts the contemporary oral tradition and belief system, captured it as an entire body of folk narrative, which existed before Greek written records. While folklore - like any aspect of culture - constantly changes, we have no way to to determine "oldest" or "youngest' myth within the body of ancient Greek folklore, because documentation does not exist in the pre-literate phase.

On the problemmatic nature of the word "myth", the following is an excerpt from my Introduction to Folklore:

Something also needs to be said here about myth. People use this term awkwardly. In a European context, myths tend to be the artificial constructs of ancient and Classical-era priests or literate people who sought to weave folk traditions into a comprehensive whole. The exercise often had political purposes, designed to provide diverse people with a single set of beliefs and stories. By reconciling similar traditions, the shared culture of these groups could be seen as more important than the differences, justifying the central rule of the king and his priests. Myth is also a way of organizing and reconciling folk traditions, which by their nature can be contradictory and highly localized. Myth tends, however, to make gods of supernatural beings, giving those powerful entities a status – for modern readers – similar to the Judeo-Christian-Islamic God, even when this comparison is not justified. Of course, it is also important to point out that myths were stories that were told – and then written down – and they were different from religion itself. Many myths were simply the shared cultural inheritance of a group of people.

In general, the word myth is best set aside when discussing more recent folk traditions, recognizing its proper status as a literary genre. Nonetheless, ancient documents recording myths can assist in understanding the history of various stories and beliefs. The authors of these texts were, after all, the first folklorists, and they were the only ones coming close to practicing the craft at the time.

Some folklorists carelessly use the term myth to denote those legends that deal with a fantastic, remote time. This primal era saw the creation of many familiar things such as day and night, fire, animals, people, mountains, and all other aspects of the present world. Folklorists properly refer to these stories as etiological legends explaining the origin of things. Sometimes, however, people interchange etiological legends with the word myth. The problem with this is that “myth” can imply something that is inherently wrong, linked to “primitive” superstitious beliefs. When the term “myth” is used for the folklore of existing cultures or for the traditions that were viable only a generation or more ago, it can take on an insulting, derogatory tone. It is best to reserve the word “myth” for ancient and Classical-era texts.