....as she tried out Batwoman's look in a ploy to hook Batman?
Lois Lane's Secret Romance
Supergirl tried to help out her cousin, who wasn't getting any closer to Lois Lane, and figured if Clark married Lois, the two could adopt her and get poor Linda Lee (who was Superman's secret weapon at this time) out of Midvale Orphanage.
Supergirl first tries painting Lois' face on billboards for Clark to see, then works on a dinner, then a relaxing boat ride, but, Superman's super responsibilities tend to get in the way of any romance between Lois and Superman.
Supergirl realizes her efforts are too much, and stops trying to interfere in her cousin's life.
This story was reprinted in Lois Lane Annual #2 in Summer, 1963, and many of Supergirl's main life events were reprinted in Supergirl Action Giants! Sadly, the original Batwoman and Supergirl seemed to have never met!