Adding coordinates to table (forcing 1:1 association without unique identifiers on either side)
PostgreSQL uses PostGIS for spatial stuff. You're in good hands, out of all the RDBMs GIS extensions PostGIS is the most powerful.

Use the Loader_Generate_Script. It'll return a table with a geometry column.

Then you just have to run

ALTER TABLE tiger.census_table ADD random_geom geometry(4326, POINT);
UPDATE tiger.census_table
  SET random_geom = ST_GeneratePoints(census_table.geom,1);


That's the easy way. It's a 5 min job. 

You usually don't want a random point though. You usually want the centroid to be useful.