You can fly cheap to Split with Norwegian Air from Kastrup Airport. Norwegian flies directly and it takes approx. 2 ½ hours from Kastrup to Split. There are lots of different airlines and agents where you can find cheap tickets to Split. If you want to fly from Germany, Lufthansa sometimes have really cheap tickets from Hamburg, but otherwise you can choose German Wings, but you must go to Hanover or Berlin.
There are good and cheap long term parking at Kastrup. You can book your parking online through CPH Parkering - it's easy and if you select a budget parking, remember that there is a shuttle bus every 10 minutes.
We have listed different airlines/agents up on this side. These are companies we can recommend. Tap the different banners to go to their website.