I have a 2005 Dodge Neon that when it is first started in the morning and after having been sitting for a while there is a rattling noise coming from the engine. The noise subsides after a few seconds and the car runs just fine. The noise seems as though it is coming from the right side of the engine if I am sitting in the car. It has not hrown any kind of codes or acted up in anyway. Just the noise. Any ideas?

Starting your engine is the worst thing you can do to it.
After sitting for long periods, all of the lubricating oil has drained into the pan and isn't were it needs to be: on the moving internal parts of your engine.
If you have this rattle on start-up, you should consider using an oil additive to help the oil cling to the engine parts longer, thus reducing the noise and reducing the possibility for premature engine wear during those cold restarts.

Try using full synthetic 5W-30 engine oil (e.g. Mobil 1). Synthetics build oil pressure many times faster than conventional oil. Also, use a filter with a silicone anti-drainback valve (e.g. Purolator PureOne).