Is there a synonym for 'fake' that has good connotations?

What's a good adjective to describe a smile which is not genuine, but still has a good connotation?

I was thinking of using fake smile, but fake has a negative connotation, which I'm trying to avoid. In fact, I'm looking for something that says the exact opposite about the person... they aren't trying to be fake towards people, they are just so kind that they don't want the other person to feel bad, therefore they put on an insincere smile to be kind towards them. Insincere, too, has a negative connotation which I'm trying to avoid, since it makes the person sound like they have negative qualities as well.

Perhaps a little background could help clarify: imagine a person that is annoyed by something that a friend does, but doesn't want the friend to feel bad about annoying her, so she puts on a smile just for show. The smile isn't meant to be [snarky, rude, disparaging, sarcastic, etc.], it is truly, genuinely meant to be so that the other person doesn't feel bad about annoying her. Therefore, as you can see, the person really is kind and using a word such as fake doesn't do justice to describe the smile.

Any suggestions?

You might say courteous or polite. Both of these suggest an action which is in some sense insincere, but which is motivated for other good and defensible reasons.

Based on the context you provided, I think I would use complaisant smile.

Accommodating, kind, and possibly custodial also occur to me, depending on their relationship.

Faux

Forgive me. I know you specifically asked for a word that means fake but has positive connotation. The only ones I can think of are generally negative, but it occurred to me that you might describe the smile in a more specific way instead. Rather than a "fake" smile, maybe it is "sympathetic" or "practiced" or "well-mannered." Like this,

While her friend continued to poke her with a stick, Maria flourished a patient smile and complimented her friend's aim.

I know it's not exactly what you asked for, but maybe it will accomplish what you want.