I don't think that Lily would have been close to Molly Weasley at all (she was in The Order, but older than her, and probably a bit of a personality clash there, IMHO). I would buy Mary McDonald, or even Alice Longbottom (this is actually my strongest preference, probably for the ironic and angsty possibilities).
I'm not so sure about Petunia. There are many indications that Lily and her sister just don't get along at all at that point in her life. In the letter Lily wrote, that Snape later finds, for instance, there is mention of Harry breaking the 'ugly' lamp (or was it vase) that Petunia had sent her for Christmas, and Lily seems amused and glad in the mentioning, almost as though Petunia meant almost nothing to her at that point. I suppose it could just be a case of Rowling doing a poor job at getting her intentions across regarding the relationship (when has that ever happened before? ;-)). But I would assume that the godmother would be a friend she was close to in The Order, rather than her sister.
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I'm not so sure about Petunia. There are many indications that Lily and her sister just don't get along at all at that point in her life. In the letter Lily wrote, that Snape later finds, for instance, there is mention of Harry breaking the 'ugly' lamp (or was it vase) that Petunia had sent her for Christmas, and Lily seems amused and glad in the mentioning, almost as though Petunia meant almost nothing to her at that point. I suppose it could just be a case of Rowling doing a poor job at getting her intentions across regarding the relationship (when has that ever happened before? ;-)). But I would assume that the godmother would be a friend she was close to in The Order, rather than her sister.