You could do a SQL Select that would calculate the areas.
MapInfo Professional also has a built-in ProportionOverlap() function that could be used to calculate the proportion/percentage.
Select BORDER.ID, CartesianArea(Overlap(BORDER.OBJ, COVERAGE.OBJ), "sq m") "Overlap"
, ProportionOverlap(BORDER.OBJ, COVERAGE.OBJ) "PropOverlap"
From BORDER, COVERAGE
Where BORDER.OBJ Intersects COVERAGE.OBJ
The above select statement should work, but if your coverage table contains more than one object, you might want to group the result by the ID of the BORDER objects and Sum() the area calculation.
Also the proportionaOverlap might not work correctly in this case.
Finally I can recommend that you take a look at the tool "ProportionalOverlap" that you can find the Tool Manager in the later versions of MapInfo Professional.