If I remember correctly (and Sue please let me know if I'm wrong here) the Coleman basket has bars rather than slats for it's flooring, which might work well with the Yakima spare tire kit. The only problem might be if the "hanger pieces" that wrap around the bars are too small, but you may not know that until you're actually looking at it in person. If the bars on the Coleman are of a similar diameter, you still may need to drill some new holes to attach the Yakima plate. But again you won't know until you compare the two racks and the kit.

If I were you (and not to volunteer Sue here ) I would meet up with Sue to compare your racks (that sounds pretty funny lol). Just take the Yakima kit off her spare and see if you can mate it up to your Coleman rack.