If you don't have too many columns, you could make cell styles for columns. Although you would define the Table as having the alternate fill; you could design your cellstyles for the columns to either allow that to show through, or else give them a fill of paper white that would override and cover up the alternating fill of the table. The idea is cover up all columns except the one you want to alternately fill.
do you start to build this table or did you already finish filling it with text and did you apply the formatting?
Can you easily cut a selected column to an Excel file to get its unformatted contents and copy/paste the contents in again formatted through applied cell styles?
If that's the case you could remove the text contents, apply two cell styles with alternate fills to two cells in that column.
Then you could copy/paste the two cells in the first step when selecting the third cell, four cells in a second step, eight cells in a third step and go on this way to format all cells of the column. When done paste in the text contents from the Excel column. Just tested that on Windows 10.