Does her employer put any parameters around how long she can use the "Paid sick time" for different types of deliveries? It's worth an inquiry to her benefits manager. For STD, mine allowed 6 weeks for vaginal birth, 8 weeks for c-section.
As for what a doctor will approve, I'm assuming most are willing to sign for whatever length works best for you. When I brought my STD forms for my OB to sign, she asked me what dates I wanted to put on them. Since I was only eligible for STD at 60% pay for the first 6 weeks after delivery, I just chose a date 6 weeks out.
FWIW, my employer offers 2 weeks of paid parental leave, then you can use any accumulated vacation. In my case, I got about 7 weeks total at full pay (6 weeks of 60% STD, supplemented 40% by sick time accrued, then 1 week of accumulated vacation), then nothing for 6-8 weeks. I went back part-time when baby was about 15 weeks old, and was back to full-time by 18 weeks or so when DH took a several weeks of unpaid FMLA leave on his own to care for the new babe. We just made a point of setting aside some cash in savings to make up for both unpaid leaves. It was really nice to be able to ease back in to work at my own pace.
Like others have said, you can't exactly plan when you conceive or deliver. Honestly, if you can manage to save up to cover the difference, I don't think it's worth it to attempt to plan such a major, uncertain life event around a potential difference of 2-4 weeks of partial pay.