If you sold covered calls, you established a "short" position. The date you "sold" the call is the date you "Acquired the position, and the date you bought the call back or it expired is the date you disposed of the position. So, you want to enter the date you acquired (sold) the call position as "Date Acquired" and the date you disposed (bought to close or expiration) will be entered as "Date Sold".
Unfortunately the Turbo Tax software does not allow you to enter the dates in this manner. It indicates you cannot have the Date Sold precede the Date Acquired. This is in essence the problem.
The terms purchase date and sale date can be re-interpreted as opening transaction and closing transaction. Thus, go ahead and use the purchase date (opening transaction) as the date you sold the covered call, and the sale date (closing transaction) as the date the covered call expired, or you closed it. In this way, the transactions will be in chronological order.
If you had a gain on the covered call, then your cost basis will be less than the proceeds. We assume the proceeds were the premium you received when you sold the covered call. If the covered call expired, then your cost basis would be zero. If you closed the covered call position prior to expiration, then your cost basis would be whatever price you paid to close the position.