I'm not currently in academia, but as a recent job-seeker I'll caution you to avoid assuming how someone else will feel about a particular job. You don't know this person, or their situation, or what their goals are. You do them - and possibly yourself - a disservice when you just assume they won't want something and don't even let them know about it.
As an example, I had a recruiter tell me (well after the fact) that I was rejected for a position because it was located 200 miles away from my current location. The company I was applying to did not have the budget to pay for relocation, so they rejected me because I wasn't local. What they did not know is that I was perfectly willing to relocate at my own expense, as the job in question was close to family and a place where I had been trying to move to for several years. Instead of asking me about it, they made the assumption that I wouldn't find it acceptable and they lost what could have been their most valuable team member (I might be a bit biased...).
As another example, my wife applied for a job recently and did not get it. After the position was filled, she received a call from one of the managers who told her that while she lost out to a candidate with more experience, they were still very impressed by her and think that she would be a good addition to their team. They told her that they were anticipating another position opening up in a couple of months and while it wasn't the same as what she originally applied for, the work was similar and she would have opportunities to move from there to what she really wanted to do. This was a much better way of handling it, as my wife had wanted to work with this organization for a long time but it's nearly impossible to get your foot in the door. The manager didn't know that, so she politely informed my wife about the opportunities and let her make her own decision.
In your case, how you communicate with these candidates is key. It's unlikely that you'd offend someone by replying with a message like
Even though we weren't able to offer you that particular position, we
were impressed by your interview and still think you'd be a valuable
addition to our team. There are several other open positions that
should be getting posted soon. I don't know yet whether they'll be
part-time positions or full-time positions, but some of them would
definitely benefit from someone with your particular background in
XYZ. Would you still be interested in working with us?
You're letting them know that you thought they were a top quality candidate, and you're simply asking if they would be interested in hearing about other opportunities. Be polite, and focus on future opportunities in general at first. Give them the chance to say "yes", "no", or "yes, but only if it's full-time" before you start talking about any specific positions. I've had many recruiters do similar things to me when discussing possible contract work (which is pretty much the industry analogue of the part-time positions you describe). Float the general concept and get a good feeling for what they're looking for before you offer them something specific that might be absolutely out of line. If they're not interested, don't push it and ask if you can contact them when a full-time position becomes available.
If you approach it like "we're low-balling you with this lesser position" then you probably will offend people. If you approach it like "we really do want you on board, and we're trying to find a position that can make that happen" (and you sincerely believe that), then you're likely to be received in a positive way.