It sounds like you need to conditionally set the blinking backcolor depending upon whether the cell is an alternate row or not. I am not sure you would be able to do this using the default blink support as the backcolor is set through a single BaseStyle.
Once option might be to handle the blinking support yourself. Below is a sample that is focused on blinking rows but you can use something simalar to blink cells. It uses a custom engine to add custom properties to each row record. Then in a QueryCellStyleInfo handler, you can use this properties to set the state for the cell being drawn. A timer is used to rythmicly redraw the blinking rows.
ManualBinkingGGC.zip