The most elaborate attempt to give one of these characters an outside love interest occurred in “Fire,” and it (cough) went up in flames. British cop Phoebe Green was introduced as one of Mulder’s old girlfriends, returning to help him solve cases, and the script included a lot of material fleshing out their previous relationship. That relationship was supposed to provide the emotional arc of the entire episode, but the lack of chemistry between these characters meant that Green was cut from the episode as much as possible.
Later on, the show tried to give Mulder and Scully other romances. We meet Mulder’s old flame (and possibly his ex-wife!) in season five, and Scully meets a bad guy who convinces her to get a bad tramp stamp tattoo in season four. But at this point, the show was simply delaying the inevitable, because most fans wanted to see their favorite characters exploring each other’s bodies rather than the latest UFO rumors.