The Rose Tattoo and Come Back, Little Sheba are both still owned by Paramount.
I say "still," because Paramount sold off nearly 80 percent of their old movies to Universal (which is why the old films by WC Fields, Mae West, Hope & Crosby, etc., are now released via Universal, even though when they start, you see the Paramount logo at the beginning).
TCM's major partner is Warner Home Entertainment. Warner Bros. owns the biggest "back catalogue" of any studio in Hollywood right now. Five times as many titles as any other, in fact.
They own the broadcast rights to the old Warner movies (obviously), plus the massive MGM catalogue, plus the RKO catalogue. That's a whole lotta movies.
You will occasionally see movies outside of this standard catalogue show up on TCM. Universal and Paramount often license their titles for airing on TCM. Sometimes, it's even viewed as a "promotional" airing, like the recent restoration of "Wings" (a Paramount title).
In any case, these are not standard titles for TCM, so they don't show up very often. I would still look for them, though. They're bound to turn up eventually ... even if it's infrequently.
"Jaws is the Citizen Kane of movies."
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