Another variant which should be listed is JENEFER, again widespread in Cornwall. This form occurs 770 times in the Cornish censuses 1841-1891, not far behind Jenifer.
I really think it might be better to say that "Jennifer" is a variant of "Jenifer" rather than vice versa. The spelling Jenifer seems to have been by far the most common one in Cornwall where the name originated. The spelling with two n's only became the most common one because of the character in George Bernard Shaw's play.