I have not been able to add any toons to a wait list for almost a week now. The last time I had this issue my wife changed our battle-tag ID but since this has already been done once I cannot complete it again.

Is there any way to fix this issue without changing battle-tag IDs?

I currently have the most recent update 1.9.9 and have tried to que on 3 different computers.

I'm having the same issue, the problem started last Tuesday after maintainace and the only premades I've been able to waitlist for have been those from my server. I believe the issue is on Blizzard's end, something to do with b.net requests not being delivered. Seems there's nothing that can be done on our end :(
This thread has a bit more info.

http://solidice.com/forums/1/topic/cant-create-oqueue-group

Its really hard to say where the issues is, as Blizz has reportedly been getting pounded this past week with DDOS attacks, which affects the ability for their servers to perform.