Styles of nursing tops. You can see that some styles of nursing tops keep the midriff and waistline covered while allowing complete coverage of the chest as well with a breastfeeding baby, like this style:
While they can be expensive to purchase new (this is $24.95 and that site currently ranges from $15 to $43), you can check thrift stores, children's resale shops, maternity clearance racks, your local La Leche league for those who might be interested in selling or passing on tops, Craigslist, FreeCycle, and many other locations to get a handful of options at little to no cost. You can also put them on a baby registry if you'll have one.
The tail end of a baby carrier like a sling or wrap would drape over it nicely. A shawl, scarf, burp cloth, or receiving blanket can all function the same way. You could also use the smart carry to carry completely below the waistline.