There is nothing in the chart itself that will do this. There are two options which may work for you, but they both have limitations:
1) add an image or a series of colored divs to your page and layer them under the chart with CSS, then set the chart's backgroundColor option to "transparent". This will get you what you want, but it doesn't work for older versions of IE (8 and older).
2) if your data structure is amenable, you may be able to use a ComboChart instead of a ScatterChart. You could create "area" data series to color the 4 quadrants and use "line" series for your data points, with the lineWidth set to 0 and the pointSize set to something greater than 0. This will work in all browsers, but only if your data is amenable.