The COIN games are great, and Cuba Libre often is named as the easiest to get into, but don’t disregard Falling Sky (gallic tribes vs Caesar) or Liberty or Death (american war of independence). I think the latter one isn’t in print right now, so if you want to get it soonish, probably CL or FS would be your best bets. I just name LoD, because especially for two players it has a great mode of play where you don’t need to add any bots – both players just play the “allied” factions and disregard the local victory condition between allied factions. With all other games from the COIN series, you probably will have to add bots to play it two players.
Another important part about COIN: even though they look like euro games, they aren’t. Be prepared to lots of rule complexity compared to even heavy euro games. But yes, I am sure they will be very different from what you have.
Another option of a “proto-COIN” would be Labyrinth, war on terror – you can play it two players or solo and with the expansion play it solo as either the Jihadists or the American forces. And it is in print right now, so should be easy to get. It is a much more political game than the COIN games even, quite a bit like Twilight Struggle.
Leaving Earth on the other hand is a totally different beast and if you are into very thinky games, this is great. It can be played multiplayer, but I really have a hard time envisioning me to ever play it with more than just myself, because I imagine the downtime being horrible. You are constantly calculating and recalculating missions. But solo it’s really great.
Another game you might want to look into is Night of Man or Conflict of Heroes, both come with expansions that add very solid solo play and both are good as two player games, too. NoM is one of my favorite tactical skirmish games with solo mode, but that might be just because I haven’t yet gotten my CoH copy (it’s incoming this week, though). NoM definitely gives you a ton for the money, and CoH adds the firefight generator as another expansion that allows you to generate your own solo scenarios and so have even more replayability. Both aren’t exactly cheap, though.