Feign means to fake, or pretend, so unfeigned means sincere. If you greet a friend with unfeigned joy, she'll know you are happy to see her.
Unfeigned is a delightful word, pertaining as it often does to young, innocent, and trusting people––the ones who cannot hide their feelings. Who wants fake laughs when you can have unfeigned laughter? Or fake tears when unfeigned sorrow is so much more affecting? When spelling unfeigned, remember the poem: "'i' before 'e,' except after 'c,' or when sounding like 'a,' as in 'neighbor' or 'weigh'." Or unfeigned.