If you do not wish to enable backordering, the other alternative is to allow customers to request an email notification when a product comes back in stock.
Navigate to SYSTEM > CONFIGURATION. On the left under the Catalog tab, click Catalog.
Click and expand Product Alerts section.
To offer alerts when out-of-stock products become available again, set Allow Alert When Product Comes Back in Stock to “Yes.”
When complete, click the Save Config button.
Now you'll want to flush cache and reindex if necessary:
SYSTEM > CACHE MANAGEMENT. Select Flush Cache Storage at the top right of the page.
SYSTEM > INDEX MANAGEMENT. Select All, Submit next to Reindex Data at the top right of the page.