If you want to find a time that doesn't compete with other major sports you can't.
You can try and work around the other sports. Sunday isn't a good idea. Saturday morning was the spot for years before being cast aside.
It would really throw the week off for a tour player, but thursday nights wouldn't be so bad. NFL doesn't have games till late in the season, and most of the college games on then are lower tear schools and games. Plus coming on in the evening like 7 or 8p would be much easier to catch then on a Sunday after noon or morning where people have church, family events and everything else imaginable to cram in on your two days off.
Plus with fantasy sports and everything else you don't want to go to work after missing something great in football and say "man did you see Walter Ray in the tenth frame yesterday?". Yes true bowlers will watch sometimes. Any more most of the people I talk with miss the show, or only catch a few minutes of it.
I really use to enjoy watching bowling. Any more I forget to record it and when I do see it I only watch for a few because the format always changes and it isn't enjoyable to watch.
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" men lie, women lie, numbers don't "