Mary Duke Building, 1909.
Built in 1896 after Washington Duke's gift of $100,000 to establish equal education for women at Trinity, the Mary Duke Building (named after Duke's daughter) was the first dormitory to house women. However, per the university archives, it soon lost its exclusivity:
"Having a dorm dramatically increased the attractiveness of Trinity for women. However, the first year was controversial but not for the expected reasons. The dorm was finished so quickly it provided more beds than there were female students. President John C. Kilgo quietly picked suitable senior men to share the facility. A professor's wife wrote her daughter, 'Dr. Kilgo has put boys in the Woman's Building so you see it has come down to a mixed boarding house already. If my girl was there I would take her away.' Later records indicate this ironically co-ed dorm may have had nine male boarders, mostly single faculty. The Mary Duke dormitory, sparked by Duke's gift, helped increase the enrollment of women to fifty-four by 1904."
(Alumni Register of Trinity College, 1915.)
Mary Duke Building, ~1900
I haven't come across any recollection from female students who lived in the building during its ~12 years. One male student wrote that the building was "a very popular place for the male students, [with] one parlor, but a dozen or more cubby holes, staircases, window ledges, and other points of vantage for courting."
One can surmise then, that Trinity as a co-educational institution likely boosted interest from both female and male applicants.
The Mary Duke Building appears to have stood until the 1909 construction of Jarvis Dormitory.