Yes, you can change the order of the tribute types when adding or editing a gift. Click on the up and down arrows of the drop-down box and click on “New/Edit”.

 
Find the value that you want to re-order and click on the icon with 3 rows that is to the left of the value. Drag the value to the new location in the drop-down and drop it in the new location. Your changes will automatically be saved.