"Profit after tax" can have multiple interpretations, but a common one is the EPS (Earnings Per Share). This is frequently reported as a TTM number (Trailing Twelve Months), or in the UK as a fiscal year number. Coincidentally, it is relatively easy to find the total amount of dividends paid out in that same time frame.
That means calculating div cover is as simple as: EPS divided by total dividend. (EPS / Div).
It's relatively easy to build a Google Docs spreadsheet that pulls both values from the cloud using the GOOGLEFINANCE() function. I suspect the same is true of most spreadsheet apps. With a proper setup, you can just fill down along a column of tickers to get the div cover for a number of companies at once.