OTR copyrights were generally done by copyrighting the script. Wyllis Cooper died in 1955, and it's unclear (especially with the many changes in copyright law in the interim) whether the copyrights for Quiet Please could've persisted to today. If such rights survive, they aren't being exercised by anyone. Carl Amari of Radio Spirits Inc, who licenses many series for sale, has said that although he has actively searched for a Quiet Please copyright holder he has been unable to find one to date.
To make a long story short, Quiet Please has most likely lapsed into the public domain but this is not known with any certainty at the moment. If by chance it isn't public domain, it would seem that the copyright holder is either unaware of or uninterested in the fact that they hold the copyright.
If a valid copyright holder does ever turn up, this site will respect their wishes with regard to distribution of the series.
The old episode MP3s, transcripts and press are presumed public domain which may be used in any way you like. Original content, like episode descriptions, re-creations of lost episodes, story adaptations, and original productions are all free to use with the condition of a linkback attribution to quietplease.org.