The side stand from an ST4S will certainly fit because it's exactly the same part number - so it won't help your problem either.
Make sure that both the side stand mounting bolts are present and that they're torqued up correctly. They should be on a new bike but you never know, and a small amount of play in the mounting can show up a lot more in how the bike leans over.
As derek says, check the rear ride height. To do this put it on the centre stand on a flat bit of ground and measure the distance between th floor and the bottom of the rear wheel. For a sweet handling bike, most ST owners have the rear wheel just grazing the floor when the bike is on the centre stand, but there is an inevitable trade off on how stable it's going to be on the side stand with the rear ride height set higher 'cos the higher the rear the longer the stand would need to be.
You may decide you value a secure sidestand over sporty handling, but you can juggle about to get a good compromise. If all else fails you can try one of these lovely things...pricey but luscious
http://www.cyclecat.com/DKS1-1.htm