The trick is to first get the general public interested in animation of all kind first. Besides, The Flintstones was a great deal more successful than those show in particular, and besides, I'd simply air Star Trek The Animated Series in rotation with the Classic Series rather than as a separate show.
Well like I said before, it's not necessarily a fact that viewers in general dislike reruns, but that:
A. Prior to say the launch of Cartoon Network and Toon Disney, classic programs were still shown on other channels, thus having a network showing them constantly was overkill at that point. Now as we all know, Toon Disney will be converting to Disney XD next year. But assumming that Disney was to try for a 24 hour cartoon channel again down the line, I think it could work.
Mainly because they have ownership of the Saban cartoons (for the time being the Marvel toons), their Jetix Original cartoons and their Disney Channel produced cartoons for this decade. Thus a Toon Disney revival would have more shows at it's disposal compared to Toon Disney's 1998 schedule.
B. Certain shows are reran too much. Nicktoons was a big offender for instance by running a 26 episode show such as My Dad The Rock Star not only every day, but multiple times in the day.
To support my theory that excessive airings are the problem and not the rerun, just look at Cartoon Network and Toon Disney. Sure they've acquired more new programs over time, but they were able to keep the older programs on their schedule longer than Nicktoons was. Simply because the formers had more shows at their disposal. Even with acquisitions and recent material like Spongebob and Fairly Oddparents, they had less than 50 shows.
I repeat, rotation would be a great way to keep the reruns from getting stale as:
A. One show would get a break while the other gets a chance to air.
B. The combined episode numbers will lower the redundancy which causes the viewers to tire of said reruns. By rotating say Doug, Ren & Stimpy, Rocko's Modern Life and Aaahh!! Real Monsters in the 7:00 AM slot, you have a combination of 208 episodes.
The beauty of rotation is that sooner or later another show will end and be able to join in the rotational block.