Some examples from New England:
For a long number of years, WGBH-2 Boston carried the Longwood tennis tournament (held just outside of Boston) and eventually fed it to PBS. WGBH also occasionally carried some Boston area college sports, especially college hockey in the early 1970's (then, as now, three of the teams usually seen on those telecasts, Boston College, Boston University, and Harvard University were/are among the country's elite men's college hockey teams).
For nearly three decades, New Hampshire's statewide public TV network (then known as New Hampshire Public Television, now known as NHPBS) carried a number of home games of the University of New Hampshire men's hockey team. The telecasts were quite popular, especially as the team during those years was a regular contender for championships first in ECAC Division 1 men's hockey and later, Hockey East.
However, NHPBS dropped the games a little more than ten years ago because the costs of production were getting too high.
Also in New England, Connecticut Public Television for years carried University of Connecticut women's basketball games. With the team having won several national titles and being perennial national championship contenders, the telecasts became extremely popular.
But a few years back, the SNY regional cable network, looking to get more cable systems in Connecticut to carry it, made a huge bid for the rights, a sum that a noncommercial broadcaster like CPTV couldn't match.
And up in Maine, the statewide public TV network (Maine Public) has long carried that state's high school basketball tournament, which as far as I know, they still do.