Is it dental related? See if you can find a few dental schools that would link to the charity with the right anchor text. Lisa is on the money, start with board members that are alumni.
Do they do any fundraisers? Anything interesting or fun? Talk about it and find places to talk about it for you. News loves heart-warming 'fluff' pieces even on the web.
Thought about an infographic? May not get anchor text value, but it could get some good in-bound juice.
Are they a big authority on anything? Do they have a weekly newsletter etc..? publish that to Issuu.com and slideshare.com
Have you looked at comprable charities across the nation? maybe some good links buried in their profiles.