In this post I am simply offer a compilation of who, what, where in terms of these languages and what I know is happening. My knowledge of these courses and institutions varies from having some personal contact, to having read and used materials, to having taken some of their offerings. I would be happy to add to this list or provide succinct but further details from any of these providers, if they would care to comment/contact me.
Conversational Koine Institute
This is largely the work of Michael Halcomb, working out of Kentucky. He offers online courses that consist of 1 hour a week for 10 weeks, teaching in a communicative method through video conference calling. The core curriculum moves through 5 levels of classes, and some academic credit is available through Asbury Theological Seminary. Also has produced a number of print resources. CKI also offers some immersion type events, typically over a weekend period, as well as Greek Readings classes.
Biblical Language Center
This is the brainchild of Randall Buth, and covers both Koine and Biblical Hebrew. Primarily it runs intensive courses in Israel, but this has expanded to some North American offerings, and produces books with accomapnying audio that can be used either in conjunction with the courses or for independent study.
Based in Jerusalem, courses include Koine Greek and Biblical Hebrew. The Greek is taught by or under the direction of Prof. Christophe Rico, who has also produced the Polis Method including at least 1, with 2 more forthcoming, textbooks aimed at conversational method teaching. Summer coursese are offered in Rome, Barcelona, Florida, and Jerusalem.
Accademia Vivarium Novum
The 'big name' associated here is Luigi Miraglia. The Accademia offers a range of full-year courses, as well as a 2 month summer intensive, focusing on active methods of learning both Latin and Ancient Greek, alongside a curriculum based in true Humanist ideals and a broad reading in ancient and neo-Latin literature.
Academy of Classical Languages
I don't know anything about this outfit beyond just stumbling upon them on the internet, but they are offering web-conferencing lessons using a TPRS approach, with Biblical and Classical Greek, as well as Latin. Course materials include Athenaze, Randal Buth's Living Koine materials, and Ørberg's Lingua Latina.
As per the comments section below, the classes in Greek use a restored pronunciation, and are structured month by month as blocks of 4 x 50 min lessons.
Is Associate Professor of Greek and New Testament at Criswell College. He teaches some Greek with a communicative approach, and blogs about Greek pedagogy, among other things.
Netherlands based, and the website is currently in Dutch, but Casper Porton is running both classes in Latin and Greek, as well as training for teachers in living language teaching methodologies.
The Association for Latin Teaching (ARLT)
This Association was founded by the famous (mildly) WHD Rouse for the reform of Latin teaching and especially the Direct Method. That's no longer quite the main purpose, but this is probably the main Association in England of interest for active Latin proponents.
SALVI (Septentrionale Americanum Latinitatis Vivae Institutum)
aka North American Institute for Living Latin Studies
A US based association dedicated to communicative approaches. In terms of educational programs, it runs a number of weekend immersions, and some newer 4-5 day immersion workshops. Has had, recently, some connection with WAYK, which see below.
Institute of Latin Studies
Based at the University of Kentucky, this is where Tunberg and Minkova are based, among others. They offer a Graduate Certificate that focuses on active command of Latin along with exposure to Latin literature.
Where are your Keys
WAYK isn't really in the Latin education game, but US based Latin teachers interested in communicative methods, especially TPR, TPRS, etc., have had some involvement in applying WAYK to Latin, including a workshop (or more than one?) with Evan Gardner. I've had some personal involvement with WAYK just in terms of learning it online and applying it in some teaching situations. So that's why I mention it here.