If you look at the IGI on FamilySearch.org - put Gardner as "Last name", then choose British Isles under "Region" and Isle of Man under "Country" (fill in nothing else) you will see a few Gardner/Gardener etc. entries, mainly in the 1800s. Look for extracted entries which are usually in capital letters (extracted from the parish register) because Church members' entries are often unsubstantiated.

Also look at the 1881 census, also on FamilySearch, and put Gardner as "Last name" and choose Isle of Man as "Birthplace Country". You will find 8 entries, all living in England. Three are wives, so only 5 Gardner/Gardener/Gardiner b.IOM.

Thirdly, try Search on Manx Notebook, with spelling differences entered, one search at a time.
www.isle-of-man.com/manxnotebook/search.htm

There are some very interesting Gardner entries there, but they don't look like an old Manx family.

Sue