The 1.06.34_V firmware which first included the iPlayer was pulled by WD due to problems.
Because of the many problems posted regarding that firmware they released a Public Beta 1.06.41_V which also included the iPlayer.
It appears that this public beta firmware is still available from the page above or the link below.
You download and unzip the WDTVLive_1.06.41_V.zip file to a folder on your computer
You edit the ver file in the 1.06.41 with notepad and change the VERSION from VERSION=‘1.06.41_V’ to say VERSION=‘2.06.41_V’ (This is only to fool the player into accepting the old firmware, it will still be the firmware 1.06.41 which is installed.)
After editing in notepad on the computer you save the .ver file.
You copy this file and the others which were in the zip file to the top level of a USB Flash drive. Only these files are to be in this top level. (normally 3 or 4 files)
Plug the flash drive into the usb port of the player.
After a short period of time an icon should appear saying that there is new firmware (2.06.41)
After installing and rebooting the player will say that there is new firmware, you can ignore this.
Eject the USB flash drive via the remote button.
You should now find the BBC iPlayer in the internet media.
Make sure that you do not update even if the player prompts you (which it will) or you will lose the iPlayer.