Seen the reviews, though I just bought CK2 this past weekend, so I'm still learning it.
My first serious game is as Tyrone (Ireland) and other than as a Sims game to breed a nice family tree, I don't quite see a path to power for a 1-province kingdom. I did successfully make the Pope my liege, and teh bastard finally lifted my excommunication after several decades of loyal service, right before my starter king died!!!! Nice guy teh pope!
My starter king and his heir both got in some nice crusader action from it though.
I tried dilligently to marry into a neighboring kingdom as a heir, but no dice. I'm thinking "breeding" my courtiers would actually be useful for improving my own family's breeding. Is that correct?
You swore allegiance to the Pope? As in, your country turned white and had "The Papacy" written across it?
Using the forged claims system described above can be pretty expensive, and while it does work for provinces that resist other forms of assimilation, it's not my favorite due to the cost.
There is the more direct method of marrying the sole female heir of a duchy/county (
not matrilinear-ly). Then, your children will inherit the target title as well as your core titles. Sometimes, that takes a little work (i.e. assassinations) to remove other male heirs, which is more expensive in recent patches but still doable. It's probably too expensive for a 1-province county.
Another method which I am coming to appreciate is to simply marry a person with a claim on the title (i.e. the female heir after a line of male heirs), and then press her claim on the throne (via a war). Then, she will reign as an independent ruler, but your children will still inherit both titles.
Tyrone can't immediately do this, but once you get one more province via one of the above means, you can claim the duchy title, which gives you a CB on the other counties since they are part of your de jure realm. That can be used to quickly expand in Middle Ireland where there are 3 (?) two-province de jure duchies--you take one the hard way, then take the other immediately since you claimed the ducal title.
The final method, which usually works for counties and duchies you are on good terms with, is to acquire their de jure kingdom title, and simply ask them to swear allegiance to you. It almost always works for counties, and while duchies try to resist (there is a "close rank" negative modifier), you can work the diplomatic angles and get them to accept. Or declare a war for unification of your proper kingdom. That's more of a long-term plan for the single province starter, though.
Of course, these methods require Agnatic-Cognatic succession laws, but I find the AI is usually compliant and enacts that early on.