Keep a diary, take a diary, write a diary?
Solution 1:
The problem here is that the number of hits Google says you have is wrong.
Using the right tool will give a more accurate picture. I searched COCA for _v* a diary, which finds a verb followed by "a diary". There I get:
- ~212 results for "keep* a diary" (where "keep" includes "kept", "keeping", etc.). Some dictionaries (such as this one) explicitly list this sense of "keep". It's really no different than "keeping records".
- ~15 results for "write* a diary" (again, this includes other forms of "write").
- no hits for "take a diary", although I could see it being used if you meant "remove": "take a diary from the pile".