If you can't find a peer or direct report from the available 'Search Participant' dialog when creating a new 1:1, it will be due to the fact that an existing 1:1 is already 'Active' or 'Scheduled' with that individual.
Frankli works from the basis that only one occurrence of a 1:1 s between two people should exist at any time. Be sure to check out the 1:1 overview page for existing 1:1's with the person you want to set-up a new 1:1 with.
You can archive or edit a previous 1:1 that you have created. If your colleague has set-up the 1:1, they will need to archive or edit the schedule before a new 1:1 can be created.