On yearly basis, you can use the typical rainfall anomalies. On monthly basis, the standardized precipitation index is an excellent tool. The National Drought Mitigation Center provides a software for its calculation which is very simple to use: http://spi-support.blogspot.ro/p/software.html

It would depend on what the aims of the research would be, but you may want to check out our early paper which developed and applied a simple Rainfall Seasonality index. This is quite simple (as you requested!), and can be based on monthly data too, but it seems to be fairly well used and cited.

Reference

Weather, vol 36, pp. 201-208,

RAINFALL SEASONALITY: DESCRIPTION, SPATIAL

PATTERNS AND CHANGE THROUGH TIME

By R. P. D. Walsh and D. M. Lawler

it is related to the scale and your research aims but in annual scale, maybe the simplest and one the best method is common moving average method and in monthly scale, SPI index can be a good option

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I've now added below a copy of that Rainfall Seasonality paper in Weather I mentioned above. The paper discusses and applies our Rainfall Seasonality index to many UK, Ireland and tropical locations for analysis of spatial differences in Rainfall Seasonality. It is also applied here to the question on change in Rainfall Seasonality (not just rainfall amounts) over time. Rainfall Seasonality over time is an increasingly-recognised important field now, partly because of the significance of Rainfall Seasonality for flood and drought risk in many parts of the world.

I hope this helps. Damian Lawler