How to ask rejected full-time candidates to apply to teach individual courses?

Don't ask them. It's a smack in the face. Advertise the position in the same place you advertised the salaried one; they will see it if they are still looking, and apply if they feel they need to.

Ask them. What other option do you have? Not asking them I guess, but then you're making the decision for them. Personally, I can't imagine being offended if you explain it the way you did above. That said, I do agree that most candidates will react the same way other answerers have ("no freaking way!") -- all the more so because they were personally recruited for a permanent, salaried position.

You should have a firm offer for a specific course rather than just "inviting them to apply" for the lesser position. If possible, personalized mails or phone calls tend to be better received than form letters.

Edit: a lot of this discussion has focused on whether offering the lesser position is offensive. I think it's not, but beyond that, the question was:

How do I get the best outcome for our students and for teachers who would be willing to teach individual courses.

Even if applicants are offended by being offered the lesser position, that has zero bearing on the students or teachers that OP is asking about. Frankly, it doesn't really matter whether the rejected applicants are offended -- this will have no real consequences. On the other hand, if even one of these applicants accepts the per-course position, that could have huge consequences for both the students and teachers in question.

This sucks, but it is the reality of the academic job market. Basically, you want to offer them (hopefully), or ask them to apply (less nice, bordering on rude), the same job but now you are going to pay them less, likely substantially less, with fewer benefits and no long term security. Now, here is the hard part. If you don't offer them the worse job, they are going to walk away thinking they were not even good enough to adjunct on a per-course basis. I think that is worse than being up front.

You just need to be up front. Say "We cannot offer you the position you applied for." Then tell them you have a much less desirable position that they are clearly overqualified for, but if they are interested you would be happy for them to apply. If you actually want them to take the job, you also need to demonstrate that your department respects per-course adjuncts, despite the university clearly not respecting them. That is the hardest part. You cannot mislead them and pretend that there is a carrot (i.e., the job they applied for and the one you are trying to get them). It sounds like you care, but hopefully you have some evidence of why they should expect to be treated fairly.