Apparently YouTube started 60p support late October. However, not all browsers are able to show the 1080p60 and 720p60 options yet. The browsers I have that can display 60p options are:
Chrome - OS 10.6.8 and newer
FireFox - no luck
Safari - Yosemite yes, Maverick no
PC - I only have Windows 8.1 at the moment:
Chrome - Windows 8.1 and highly likely Windows 7 also
FireFox - no luck under Windows 8.1
IE - Windows 8.1 and highly likely Windows 7 also
Still, the most reliable way to show 60p movies online is to embed the mp4 files on your own web pages - no issue with all major browsers except Mac version of FireFox.
YouTube may also support 48p, but I’ve not come across one example yet. Perhaps the next Hobbit trailer since the movie was shot in 48p. 2.7K 48p will do until 4K 60p and 48p become affordable.