I have wasted many hours looking for the answer to this question. Anne Catherine Emmerich said when St. Joseph's body is discovered, it would be a great joy in the church.

I have read of him possibly being buired in Valley of Josaphat where other notable Bible names are found. [link to en.wikipedia.org]

Nazareth was another area where they thought he might be buried.

It is a mystery, I even wrote Mel Gibson that he should invest in a documentary into the search of it.