Until the mid-60s (with the success of shows like "The Beatles" cartoon), most made-for-TV cartoons aired in varying timeslots (early weekday evening hours, etc.), with some material made for Saturday mornings. After the mid-60s, newly made TV animation became the near-exclusive province of Saturday mornings.
The first made-for-TV cartoon was "Crusader Rabbit" (a series of made-for-TV shorts coupled with live-action programming/old theatrical shorts), which debuted in the late 1940s and ran through the 1950s. Other such shorts were made for TV in the 50s, but it took until "Huckleberry Hound" in 1958 for an actual half-hour made-for-TV cartoon to debut (and prove to be a big hit).
Walt Disney's first TV show was the mid-50s series "Disneyland", but (like all the other incarnations of the various series lumped generically under "The Wonderful World of Disney" name), it wasn't exclusively cartoons.
Even when color TV came along, black-and-white theatrical cartoons (Popeye, etc.) still had a home on many local TV stations through the 80s... all cartoons made for TV, of course, were made in color (even if just broadcast in black-and-white in the 50s/60s).