There's a FB group entitled Reformed Study of Church History. The main fellow behind it narrates a lot of Puritan works and uploads them gratis, and has apparently been doing it for some time. Here's the link:
https://m.facebook.com/groups/423103271047559?tsid=0.39151905664185593&source=typeahead
EDIT: And after browsing through that FB group for a moment, someone had linked to
http://www.puritanaudiobooks.net/. That might fit the bill!
I also have a Puritan Hard Drive (which was a gift several years ago). It has a lot of Puritan audiobooks on it, which is nice. However, each file is an audio billboard for SWRB; and given the past ethical murkiness surrounding them, I'd be inclined to look elsewhere.