Did you research Farming and did you have enough money to build it?

I had 12 city's at the time, all which I built farms in. it was like this I captured the enemy's city, and they had build it not next to the farm squares but one away, so instead of appearing like this (Excuse the crude Diagrams, the { } are blank spaces for building C is the city F is the farm slot, and H is house)

{ } { } { }

{ }  C   F

{ } { } { }

It was like this when I captured it, there was no farm option

{ } { } { }

{ }  C  { }  F

{ } { } { }

so I expanded the city like so

{ } { }  H  H  H

{ }  C   H  F  H

{ } { }  H  H  H

To encompass the farm slot, however this did not work either still no farm option for building. 

so escentially I ended up with a city with houses encompassing one of those slots you build farms on, with

no option to build a farm. At the time I had around 115000 gold, so money was not the issue.

I've seen before that farms aren't in the list when you expand next to them, but if you close the construction screen and go back to it, farms will be in the list.  The same thing happens with shards.  Is this something different?

Also, there are limits to the number of large tiles a city can occupy.  Your diagram must not be accurate, because a city cannot have more than four other large tiles.  If you meant the small tiles, there would be two houses between the city (which occupies 4 small tiles) and the farm (also 4 tiles).

It sounds like you used up too many of the large tiles to me.  Its a rather strange mechanic and not very intuitive.  A level 3 city can only expand into 4 large tiles.  A large tile is one farm/crystal/mine or 4 small buildings.  Once you have placed buildings in 4 different large tiles you can't expand to any more large tiles, even if you haven't filled the tiles you've used.  It's definitely a little wierd.  I'm not sure if demolishing buildings will open tiles up.  That should probably be tested.