Furniture and Furnishings - Repair Antique Table?

I have an antique Singer Sewing Machine table that has a wood top with hardwood veneer on it. The veneer is about 1/8" thick, and has delaminated around the edges of the table. Is there a way to restore it?

You mean the veneer is pulling away from the table? You can tack it back down with contact cement.

Using a knife blade, push the point under the veneer and scrape out any dirt or glue that may be loose.
While slightly lifting the loose veneer with your knife, put in some brown carpenter's glue. When this is dry, it shows a lot less than white or yellow.
Press down on the veneer and wipe away any excess glue that comes out. Lay some wax paper over the area and then a wood block on top of the wax paper. Then clamp the block down using a c-clamp. The wax paper prevents the glue from sticking to the wood block and the wood block pressed the veneer evenly and flat.
Work your way around the table in this manner until all loose areas are glued firmly down. Remove any excess dried glue with a sharp scraper or knife.
Just take your time and it'll come out just fine.

Good luck,
CD