It depends on how necessary they might be to your future success. If they no longer need to mean anything, then just conquer them.

Honestly, generally I try to stick to my original plan. If you simply tell them that you don't want to attack them and you'd rather have them as an ally, that they'll get nowhere by attacking you and everywhere by working with you; then follow it up with the notion that you value your alliance and still wish it to continue, most people will cease the attack and do as you need, giving you opportunity to stab them later.

They don't seem all that useful to have around. Unless your units are desperately needed elsewhere such a player has successfully nominated themselves as ideal territory for expansion. I'd only try forging a serious alliance with such a player if things looked very bleak with everyone else.

Usually I decided that they have now given me a legitimate reason to take over their supply centers and use the new units more efficiently under my command. I may not stab an ally, but once they have done it to me, then I don't have to be nice anymore.

When it happens, you just drink one beer.

If you adopt the aforementioned strategy, you will be drunk by the time you finish a live game with MichiganMan.

I kind of agree with that. MM has some pretty visionary ideas sometimes.

Depends. If they're more useful as a non-enemy and can be reasoned with then go for it. A lot of people make the tunnel-vision mistake that once a stab attempt happens that cements the path, but doesn't have to be. Don't be afraid to swallow your pride and forgive, sometimes it even puts the onus on you to rebuild the relationship and do all the heavy lifting to make friendly with your stabber but if that's what's best for your game do it. These things aren't personal, everybody has attempted attacks on friendly (or neutral) players before, people who take self-righteous attitudes towards being betrayaled seem pretty foolish in my eyes. Then again if it makes most sense to take advantage of commencing a war without having blood on your hands then by all means go for it, but really no rush for that since you can always reference the earlier stab as justification for your subsequent attack later on the game. It's not a bad IOU to have in your back pocket.

Besidea, sometimes forgiven stabs can lead to very strong alliance bonds if you handle it right.

Those are my thoughts VI.

If it wasn't in my plan to stab them now, then I feel that it's worth it to try to redirect the player back to my original plan. I've found it rather successful. If they agree to quit the stab, then you're all the better for it, imo.

Don't try to change course unless you have to. Usually, an ineffective stab is not a 'have-to' situation. After all, it was ineffective for a reason.