I've managed to get BBC iplayer working on CM 7.2 
This is the very latest maintenance release by Alquez, by the way.
Make sure you have checked 'Unknown Sources' in Settings > Applications
First of all you need to download the version of Adobe Flash 11 from Adobe Flash 11 for Wildfire S (works) - xda-developers
and reboot the phone
Then download the Android iPlayer app from my Dropbox folder http://dl.dropbox.com/u/32324426/bbc.iplayer.android.13014.apk (you won't be able to download it from the market because the market will say it is incompatible with the WFS) and install.
I tried iPlayer through both the stock Android browser and Boat Browser - the programmes would open, play for about 5 seconds and then the browser would crash. The app works OK, though you may get a message when you first open it telling you that there is an update available - choose update later.
I tried viewing a video on dailymotion, however, and that played fine.

This is the very latest maintenance release by Alquez, by the way.
Make sure you have checked 'Unknown Sources' in Settings > Applications
First of all you need to download the version of Adobe Flash 11 from Adobe Flash 11 for Wildfire S (works) - xda-developers
and reboot the phone
Then download the Android iPlayer app from my Dropbox folder http://dl.dropbox.com/u/32324426/bbc.iplayer.android.13014.apk (you won't be able to download it from the market because the market will say it is incompatible with the WFS) and install.
I tried iPlayer through both the stock Android browser and Boat Browser - the programmes would open, play for about 5 seconds and then the browser would crash. The app works OK, though you may get a message when you first open it telling you that there is an update available - choose update later.
I tried viewing a video on dailymotion, however, and that played fine.