Southwark Theatre in London has just announced their new production of Dear Brutus, 29 November-30 December 2017.  From their website:

“The fault, dear Brutus, is not in our stars, but in ourselves.”

1917. In a remote English village there are rumours of an enchanted wood. One of the inhabitants – a mysterious old man – invites eight strangers to stay. They all have something in common. When, one evening, the wood miraculously appears the guests feel compelled to enter. What happens there has the power to change their lives forever…

From J. M. Barrie, the celebrated writer of Peter Pan, The Admirable Crichton and Quality Street, comes this haunting drama of self-revelation. Darkly comic, and presented in a sumptuous production for the play’s centenary year, Dear Brutus is Barrie at his most magical."

http://southwarkplayhouse.co.uk/show/dear-brutus/

More coverage about the announcement here:
http://www.playbill.com/article/j-m-barries-dear-brutus-to-play-london

https://www.broadwayworld.com/westend/article/J-M-Barries-DEAR-BRUTUS-Comes-to-Southwark-Playhouse-for-Christmas-season-20170907

https://www.londontheatre1.com/news/181201/j-m-barries-dear-brutus-comes-to-southwark-playhouse/

Hello, and welcome to the forum. I'm one of the moderators on the site but am afraid you wouldn't find much information about JMB's ancestry here, as it mainly concerns his works and his relationship with the Llewelyn Davies. You might be more successful if you contacted the Kirriemuir Heritage Trust (or even the Moat Brae Trust) as they might have more information and contacts about the family, and point you in the right direction.

http://www.kirriemuirheritage.org.uk
http://www.peterpanmoatbrae.org

Over the years, there have been other people researching their family ancestry and links with the Barries, so if you scroll down the "J M Barrie" sub-section in the forum, you can read posts and questions about his genealogy, and possibly contact them via their emails.

I hope this helps. If I think of other sources, I'll post an update.

A literary society dedicated to J M Barrie has been founded and will be launched officially on 9th of May, which is of course his birthday. See http://www.jmbarriesociety.co.uk for more details.

Until now, there was no real Barrie Society so it's wonderful news. We hope many members will join and get involved, and that the society will flourish, both in the UK and internationally.

Follow it on Facebook https://www.facebook.com/search/top/?q=jmbarrie%20literary%20society

Sorry, I should have added that even if Samuel French no longer represent the Barrie estate on behalf of the Asquiths, they should still have the contact details in their database or address book. Someone in the agency must know, as they would have paid the estate royalties for plays staged in the UK to the estate until the end of 2007, when Barrie's copyright expired. (Several of these plays, such as Dear Brutus, Mary Rose, What Every Woman Knows were staged before then.)

The London theatre agents Samuel French represent the Asquith estate for all non-Peter Pan plays and might be able to help you with a contact. www.samuelfrench.co.uk

Otherwise, as Andrew suggested, you'll have to track down Herbert and Cynthia's descendants. The website www.thepeerage.com is helpful (although not very user-friendly) for finding out the names of the children of Michael and Simon Asquith but doesn't of course give any other detail. However, I do remember Ivon Asquith, one of Simon's sons, used to work at Oxford University Press but a quick search indicates he may now be at Edinburgh University Press.

If you do find out more, please could you post any details on this website, for future enquiries? Many thanks!