Consequences, by Julie (you definitely don't want to miss this one!)
The Beauty And His Beast, by Cathy Roberts (a twist on the fairy tale)
The Ghost Of Christmas Present, by Cathy Roberts (Christmas Day starts something new for Luka and Carter)
Desperate Vigil, by Cathy Roberts (Season 6. It follows up on "The Ghost Of Christmas Present", picking up on Valentine's Day and ending right after the episode "May Day".
Waiting For A Valentine, by Ceindreadh (This is part of a larger series about Luka and Dave, but this installment has Carter in it)
Changes In Latitudes, Changes In Attitudes, by MonaCK and Cathy Roberts (it's a Dave/Carter fic. No, it's a Luka/Carter fic. Who knows how it ends up?)
The Bar, by Elamae (the first chapter of what will hopefully be a series. Who should Carter meet in a bar -- Luka, of course.)
Some of these stories were mentioned in a previous post, but weren't available on the site then, and they are now. If you go on the site and search for Luka or Carter stories, you will get returns for stories that I still need to restore. For instance, Kathryn Parsons has several Luka/Carter stories, but the stories themselves need to be restored to the site and aren't available right now.
Enjoy your reading!