If someone wants a .LY TLD (top level domain) or .IO TLD, how do I determine which domain registrar (e.g., GoDaddy, Register.com) supports the purchasing of this TLD?
If you are looking for a registrar for a niche domain the best way could be you visit the Registry's web site. These may list authorised registrars. The problem with going to non authorised registrars is that they will in turn have to go via a authorised registrar and that will only put up the price you pay.
UPDATE 13/3: The best place to find a list of registrars is the Registry's web site which is normally located at http://www.nic.[TLD]. There is a list of ICANN-Accredited Registrars which can be found at http://www.icann.org/en/registrars/accredited-list.html
Hope that this helps.
Jonathan