Back in 2014, the best (if not only) option for patching the Linux kernel without rebooting was KernelCare, a tool developed by our partners at Cloud Linux.
The situation has since changed quite a bit as live patching has officially been included in the kernel as of version 4.0. The tools kpatch and kGraft, which were still in development in 2014, have also been massively improved. Kpatch was even added to the official repository and in Ubutnu 16.04, it can be installed from the default package manager. Canonical has also recently released their Canonical Livepatch Service, which can be used to patch the Ubuntu kernel without rebooting.