These are the rules found on Wikipedia:

"1. One of the person's parents was a U.S. citizen when the person in question was born
2. The citizen parent lived at least five years in the United States before the child's birth
3. A minimum of two of these five years in the United States were after the citizen parent's 14th birthday."

In addition wikipedia posts:

"A person's record of birth abroad, if registered with a U.S. consulate or embassy, is proof of citizenship. Such a person may also apply for a passport or a Certificate of Citizenship to have a record of citizenship. Such documentation is often useful to prove citizenship in lieu of the availability of an American birth certificate."

However, I don't know if a US consulate or embassy would be willing to register a birth in which the name of the citizen parent is unavailable or the citizen parent is not there to register it. I would recommend calling the closest US embassy to find out if they can shed some light on the matter.

Perhaps you could take business trip to the US during your last month and deliver here? If you can get a US birth certificate issued, the baby could be considered a US citizen.

Best of luck!

To be on the safe side I suggest you give birth
in the USA. That way there isn't any questions.

This is not possible. For your child to have dual citizenship, the parent must pass their citizenship to their child, as stated above there is restrictions even for children born to married parents where one is American. You cannot claim this from anonymous donor as he is not legally a parent to your child and will not be on the birth certificate. Your best bet would be to give birth in America, though you will have to pay the hospital fees, which could total up to $20,000. in my opinion i would save the hospital costs and help your child apply for a school visa/work visa when they are old enough, it could save you literally tens of thousands of dollars.

This question will be answered by the clinic where you get the treatment. But as far as I know, if the baby born with the donor sperm and the baby's citizenship will be decided as per the mothers identity. So, even if you have the treatment in USA the baby would get the citizenship as yours.
Probably you would get the better answer where you get treatment.

What's wrong with being a Canadian? A lot of people in this world would love to be allowed to have Canadian citizenship. Some of them even live in the U.S.