Came across this old thread when searching for something else and just wanted to update it to say that Eva absolutely does allow the use of car seats. We flew them in March 2010 and June 2008 and used a Britax car seat both times. The FAs had no problem with it and were very helpful each time
They were also fine with us using the CARES harness for our slightly older child.
Just didn't want anyone to come across this and think they wouldn't be allowed to use a car seat. It is so much safer for an infant or child.