What can I do to cover this corner

what room is the corner in, cannot tell from photo

You would have to measure it, but they do make some decorative wood and plastic corner pieces that might fit that. You would need liquid nails for the tile side and glue the other side or use trim nails. measure the length at home before going to the store and they will cut it to length for you. Go to the wood trim isle,and then an isle where all the trim is painted white, that is plastic, not the flooring isle. You will have to look around. Remember when measuring it will not go all the way into the corner, so give your self a little room for error.

Sorry I looked at this picture wrong,, it looks different small than it does big. The only thing I can think of is there is an isle that has pieces of all shapes of metal. If you could find a U shaped piece that would slide over the tile and drywall. And glue it on, prime and paint it. They sell the metal at most hardware stores. Either that or find a piece of U shaped material that would fit inside and get a small tub of drywall putty and try to smooth the edges, sand then paint. If you had a carpenter that had a table saw he could make you a piece out of wood. Sorry for the miss understanding. I hope you find something that works. JR

What about a piece of quarter round to cover it?

If you are not adverse to using wood you could take 2 strips of 1X2 cut to the length you need and attach together (with small nails or glue) in the manner to create an L shape. Then you can paint the wood and attach to the corner with adhesive on the tile and nails into the sheet rock. If you don't like the bulkiness of the wood you may be able to find metal L shaped lengths and then use adhesives to secure the metal to the corner. I would suggest you take the picture to your local hardware store and they may be able to help you find something that would work to your liking.

Take a piece of the tile to home depot and find a colored caulk that blends into the background of the tile. Use a non-sanded caulk. If a big box store does not have a good selection of caulks a "tile" store will. Run the caulk down the edge and smooth with your finger. The ugly edge will almost disappear!

You could make a faux wood beam cover out of styrofoam to protect all the corners and add a little extra decor design. Just a thought. Good luck.

Have you thought about butting two pieces of fancy moulding to meet in the corner? The moulding could be glued onto each side.