Before you spend money on a new camera:
– are you pre-focussing by pressing the button down until you feel resistance (usually the camera will bleep) to let it get the shot set up? Do that with it pointing at where you expect the subject to be, keep it held down then when the subject is where you want it, press a bit further to take the shot.
– does your camera have a sports mode (usually a running figure in the menus)?
– does it have any manual controls, especially over ISO settings? In low light (esp under tree cover) the camera wants more light so will force the shutter speed to be longer otherwise the pic will be too dark. This can be counteracted by increasing the ISO setting (more light sensitivity at the expense of graininess) or more aperture (a bigger opening in the lens, but with a narrower depth of field, so focussing has to be spot-on).
Sorry if it's stuff you already know, but I see way too many people mash away at the shutter release with all settings on auto then complain their camera is "too slow" and misses the shot. 10 mins reading the manual can bring a huge improvement in your pics – just about any camera from the big names in the last 5 years will be able to take reasonable action shots in normal lighting conditions. Spend money on a new camera and mash away on the buttons and you'll still be taking poor shots.