I would provide them with whatever they ask. I don't think there is any way around it. Even though they state you only need to provide police certs for countries you have resided in for 6 months or more, I've read that they have requested police certs for those who have resided for less than 6 months.
I am a UK citizen and had to provide police certs for both Australia and USA, so it is def possible to apply even if you are not a US citizen.
Follow the instructions on the link. Also you will find an application form here
http://www.fbi.gov/about-us/cjis/background-checks/background_checks. You can also print the fingerprint card here too; although they will accept fingerprint cards from your local police office too. Make sure your prints are clear, when you get them done, as unclear prints can lead to delay and possibly having to have them redone. Complete the application form and include the finger prints, copy of ID and fee to the address at the link above.
It only took 4 weeks for me to get my cert (including overseas posting time)... so waiting times are fairly short at the moment...
Good luck!