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What was David Cunningham's address according to the birth certificate?
There is a David Cunningham, shepherd, aged 29, in Contin in the 1881 census and he is still in Contin in 1891, aged 39 and unmarried.
I don't believe that Jessie b 1876 is the mother of Jessie Ann or Annie Jessie Mackenzie or Cunningham b 1887.
The birth of Jessie McKenzie, mother's maiden name Matheson, was registered in Fodderty in 1876, the 40th birth registered in the parish that year. The total number of births registered in Fodderty in 1876 was 43. Therefore Jessie was born towards the end of the year.
Annie Jessie Mackenzie or Cunningham was born in October 1887. Therefore she was conceived early in 1887. That was only a couple of months after the 10th birthday of Jessie b 1876, and Jessie b 1876 was probably still only 10 years old when Annie Jessie was born.
So I don't think 'lodger' and 'friend' are attempts to cover up a closer relationship. 'Niece' in 1911 does imply a relationship - perhaps she was a great-niece?
Roderick Mackenzie, aged 93, son of Roderick Mackenzie and Christian Macdonald, died in Fodderty in 1916. There is a matching baptism on 12 April 1826, and he had two brothers, Murdoch b 1816 and Hector b 1829. Perhaps the errant Jessie Ann was a daughter of one of these brothers? Or of another sibling whose baptism is not in the surviving records?