Hello SJ! "Applying" is sort of a two part process :)
To apply to the kinship itself, please ask in-game on the coursera user chat channel (see this post if you aren't familiar with LOTRO user chat channels). Any officer can invite you to the kinship.
To apply to become a member of this website, please use the 'Apply to Kinship' link on the upper left side of the home page of this website (right under the heading 'Membership')
The process is two parts since the website is also used by many of our Coursera friends who are in other kinships.
Looking forward to meeting you in-game!