The Kings Island "Crown" logo was used through fall 1971 to promote the park. By December the new, more familiar, "Disneyland font" logo was in place. (More about that in a minute...)
Ads for the KI preview movie that played local theaters used the new logo as early as Jan 1st. However the movie itself was produced in 1971, and used the "Crown Logo" in it's title shots.
Here are samples of the logo in the variations of the "preview" brochure that was distributed before KI opened. There were at least 3 variations of the brochure. The first (far left) was distributed at Cincinnati's Coney Island at the preview center in early summer 1971. The second version was also distributed at the Coney preview center late season/August 1971. (It names the Jack Nicholas designed golf course at Kings Island which was announced in August 1971.) The third brochure was distributed at the information centers after Coney closed (note the original planned opening date of May 6th which did not happen.) As you can see, the second logo was in place for this brochure.
The new logo was developed, as I understand, in fall 1971. It utilized a variation of what's become known as the "Disneyland" font. It *may* have been suggested by Bruce Bushman, who did quite of bit of concept work for the park. (Mr Bushman was one of the original WED Imagineers responsible for the original design of Fantasyland for Walt Disney. He was instrumental in also designing Kings Island and, no doubt, patterned parts of KI on it.) The new logo could also have been a "nod" to the fact that Kings Island - when it was being announced/built - was being billed by many as Ohio's version of Disneyland.
While the park was under construction, there were 2 different billboards placed by the interstate to mark the location of the park. The first billboard featured the "Crown" logo. The second also used the "crown" logo as well - but the Eiffel Tower had become part of the advertising campaign. Here are pictures of both billboards courtesy of KI50MOVIE...
Its worth noting that ALL advertisements of Kings Island at Cincinnati's Coney Island used the "Crown" logo. Including the "Racing Coaster" billboard that sat adjacent to the Shooting Star's station.
By the time KI opened in May, the "Disneyland" font version of the logo was the only one being used for advertising purposes. The confusing matter is, the "Crown" logo still cropped up on merchandise and shopping bags etc. That (very likely) included the "Tiki Mugs" mentioned here. The reason? Because many orders for merchandise and various items were placed prior to the logo change to meet manufacturing timeline requirements.
BTW - the "Crown" logo still crops up as a "throwback" on merchandise from time to time. For instance, this season there is at least one item (a slinky toy) that features the "Crown" logo being sold in the shops on International Street.
For posterity, I think the switch to the "Disneyland" font logo including the Eiffel Tower was an excellent decision. Its far more iconic and dynamic than the "crown" logo. Frankly, I still prefer it to any logo the park has used since - including the Paramount version and the current Cedar Fair version.