I would only use 2x8 construction lumber to build a picnic table with spaces between the boards since they will shrink and move quite a lot. Construction lumber really isn't suitable for such work. If you had the correct FAS KD lumber. Most would not use any joint when gluing up a top, just fit each board perfectly to the next and glue them. You construction method for the table has to account for movement. If you feel you must have something other than a proper fit, use a spline, or two.
If I was to cut T&G on longer pieces of 2" lumber, I'd use a slotting bit for the groove and stacked dadoes on the table saw for the tongue, cut from both faces. Hand held router on the slotting bit, not a router table. Cut from both faces on the slotting bit to center the cut. If the boards aren't perfectly flat and straight, on a router table, you won't get an even cut, it can ride off center.