blizzrd
Micromanager
I failed on Khimer several times. The first two conditions are easy enough, however, spreading Buddhism was beyond me. I will get open borders with all of Europe, but those guys would run Theocracy 2/3 of the time and it takes forever for the galleons to get from SE Asia to Europe. Then stability over the long period of not growing causes pagan and other cities to flip. Does anyone have any suggestions about that problem?
For the Theocracy issue, it isn't an issue. Enter their territory and gift the missionary to them. They will spread religion to their largest available city. This is a neat little trick, but works. You can save a turn of missionary movement sometimes also, as you just have to get to the border and then can start building another missonary.
For the stability, I recommend slowly settling Australia. There seems to be little penalty due to no other civs home area being affected by your growth with this strategy.