Your best bet is to convert the corel draw file to a DXF and then import into MapInfo using universal translator. Adobe Illustrator can export to DXF, although you may have trouble importing from Corel (this will depend on your version). Try and split the document into layers from within a vector editor if you can, and convert them individually.
As an alternative to illustrator you could use inkspace which has a dxf export plugin.
If you are working with polygons an alternative would be to set the color differently for each polygon and then create a very high resolution raster from within your vector editor. This raster could then be georeferenced and vectorised. This sound like a cludge but can yield surprisingly good results. By rasterising you reduce the potential problems that could occur in the conversion process, and have a well understood work flow.