Usually, in cases like this, there are a couple of options. Often, some money is put into escrow for the repairs. Often it's 150%-200% of the estimated repairs. Once the repairs are done, any excess is refunded to the seller. (In fact, thinking back on it, when we bought our own house a while back, we did that for some chimney repairs.)
If the buyers are confident that the repairs will be done--properly and by a professional--they probably won't object to that approach.
Again, though, talk to your Realtor. These things happen, and almost always get worked out.
Hope that helps.
If I were the representing the buyer, I would recommend they wait until the repairs are completed to their satisfaction. Once they have closed on the property, it is typically more difficult for the buyers to get sellers to complete the work.