Diagnose the actual cause of the problem. What clues led you to the generator? Have you tested the battery? Has the charging system been load-tested?

Do you think the battery is any good? Another issue could be a battery drain, overnight? If there is a drain, you pull/replace fuses one at a time. When you pull the fuse on a faulty circuit, the excess drain goes away. The drain could be a light on, somewhere? Interior--under the hood--in the trunk. The old way to check for battery drain was to take a battery cable loose, use testlite between cable and battery post. If the lite comes on, you have a drain. When you pull fuse on the faulty circuit, the lite goes out.