Tables with FK's of each other
For just the country/capital relationship I would go with option 1 and allow the capital to be NULL for a country record, rather than introducing an extra table. In both cases you are allowing the capital to be undefined at any given time so there is nothing to chose between the options from the completeness and referential integrity points of view.

If you do go for option 2, if the country column is not your PK make sure it is set to be UNIQUE otherwise you could accidentally end up with two capitals. With an extra "relationship type" column you could offer extra flexibility with this table though, by allowing things like "second city" and "religious capital" (some countries have this separate from their political capital for various reasons) to be defined.