Doesn't sound like a typical CPS symptom. Could be TPS...it's located right on the throttle body and takes all of a minute to change. However, the TPS should give you an engine code if it was bad.
Before you do anything, try changing your fuel filter. This is something that should be done regularly (I change mine every 10,000 miles or so) but most people never even think about it, let alone change it. A plugged fuel filter is like any other filter...it will work very inefficiently and you'll have reduced fuel pressure as a result. At light acceleration your car will stumble because it's not getting enough fuel, as you press the gas you get more fuel and away you go. As the filter gets more plugged the car will continue to run worse and worse.
A plugged fuel filter can also shorten the life of your fuel pump, since the pump needs to work harder to send fuel to the engine.
The fuel filter is located under the car near the passenger rear wheel. It's similar in shape and design as an oil filter...it costs about $10 and takes 10 minutes to change.
I'm not saying this is the cause of your problem...honestly there could be several reasons for a low RPM stumble. But a plugged fuel filter is a common problem, and it's a good place to start since it probably needs changed anyway.
