Wikipedia seems to do it like this: when you login, they show you a success page with several images (icons of their daughter sites); the image URL itself contains enough information to log you in there, so it will basically log you in there nōninteractively as soon as your browser loads the image. (If I understand this correctly.)
This would be a nice fallback to have.
(Meh. And I would love to use the site with Lynx, but I think there’s more problems than that. This question pertains to Opera 9, which is about the newest somewhat-reliable “modern” webbrowser I can get on my OS.)