The first method (having your capital sieged) will work if you only have two cities, your capital and the newly settled city. If you have three or more cities, then your new capital will be whatever the largest city is after your capital is sieged.
Option 2 is not yet possible (you cannot voluntarily switch your capital).
However, I'm not sure why which city is your capital is so important to you. As far as I know, which city is the capital only matters when you've achieved your tenth city and achieve a special discovery applicable only to the capital OR when you use Tenaril's. Other than that, which city is the capital is of no significance to game mechanics. Does anyone else know of a reason which city is the capital city might be important with regard to gameplay?
If your concern is about getting more than 7 food squares for every city including your capital, your only options would be to exodus your first city onto a 7 food square or to have your first city sieged and then rebuild on a 7 food square. In either case the new city would not be the capital (rather your second largest city prior to the siege or Exodus would be the new capital). However, as I said above, which city is your capital will not have an effect on gameplay.
If your goal is to have a 7 food square on a mountain or forest by use of Tenaril's spell, you can build your second city on a 7 food square, Exodus your capital city (probably also onto a 7 food square), then Tenaril's your second city (which is now your capital and has 7 food) onto a mountain. However, this would still leave your former second city as your capital, albeit a capital on a 7-food mountain, and this is not the result you said you desired.
Again, from a gameplay perspective, I'm not sure why that would make a difference.
Edited by Rill - 24 Dec 2011 at 03:21