You would be able to run an auction league on yahoo. I was in one last year, but we are now switching over to cbssportsline. It can work.
You can just lock all the teams so they can not do add/drops. From there, you could run your FA system through email, getting all members of the league to send you their bids by, say, 7pm on Sunday. I am not sure if you were sending emails with them before, or anything like that, but I know if the kids don't have their own emails, they can send messages through the yahoo system as well to you. You go in Sunday night, add the players to the respective teams, and you, or they can adjust their lineups. Another option would be to have the FA bidding be open, and done on the 'league message board' on the league's yahoo website.
Hope this helps?