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Second, can you offer them anything? A coffee mug and T-shirt? A cruise? ;) Some site owners might go for another inducement.
Third, if you have the time and budget, you could also set up a new site someplace else, and come up with a plausible reason to explain why the recip links will be on this other site. It would have to be a good site, of course, with some on-topic content. Theoretically, it might work even better for the link partners if the new site was highly focused and optimized.
Some site owners will just link to you if you ask nicely. When all else fails, grovel!