How many miles on the engine? Some clicking is to be expected, and often can be remedied by changing the oil. It only holds about 3 and a half quarts, so I would try using a lighter blend...say 5W20 (assuming you're using 5or10W30). Clicking/tapping can be worn lifters(tappets) or sticking tappets or valves, or simply wear and tear on the valvetrain. I have seen engines show a huge noise improvement just by changing the oil and adding a bottle of Rislone oil treatment. Sludge and dirt buildup in the system can aggravate the valvetrain causing ticking, tapping, noises. You want to find an oil treatment that is designed for the valvetrain, NOT the lower end like the old STP ring treatment stuff. One type works to clean up and free up the valve train, and the other works to thicken oil and swell seals to reduce oil burning or loss. Just changing the oil to a lighter type might serve the same purpose as the Rislone. 5W20 will not hurt your Rio by any means. You might also check your timing belt and make sure it isn't loose/missing teeth, and causing the valvetrain to be slightly off. It isn't that hard to pull the valve cover off the Rio and physically look into the camshaft area. See if it looks dirty, sludgy....and see if there is anything odd there (probably not that you would see, but WTH?). I believe there is a ring screwed to the exhaust cam that the cam sensor reads , that can come loose, but this typically causes driveability probs and a check engine light.
Just change the oil/filter and see if it improves. Next step is additive....and after that if the noise remains the same or gets worse, you may need to consider head work.
Also remember that the fuel injectors can make clicking noises but they are not nearly as loud and obvious as the valves.