Water hardness does tend to naturally drop as a tank matures, particularly if you put lots of bogwood in there (bogwood is an absolute must if you have tetras IMHO).
However, lots of people keep cardinals in hard, alkaline water with apparently no problems. The trick is to get fish already acclimatised to local water conditions (ie. not straight off the plane, but in the LFS or suppliers for at least 5-6 weeks before sale).
My experiments have revealed that mucking about with my water is more likely to lead to disaster than leaving well alone and letting the fish get used to the way things are. Some of my cardinals are 6 years old (80 in human years) and for most of that time there previous owner kept them in rock hard water with a pH of between 7.5 and 8.5.
Some advice I did recently receive about cardinals flies in the face of what others might suggest: don't use a quarantine tank where you're adjusting the KH, GH and pH downwards over a period of weeks. Each transfer (from the wild, to a transport box, to the LFS quarantine tank, to a bag, to your home quarantine tank and finally to your main tank) has a risk of losing the fish so it is better to reduce the number of changes as much as possible. The best LFS around here recommend to put the fish bag in the main tank and swap over a cup or so of water every 10 minutes until they are used to the new conditions. I tried it the "proper" way once and lost loads of fish, and I've tried it his way and not lost one. YMMV.
You could also try peat filtering - either pre-filtering before adding the water to the tank, or peat granules in your filter. However, if your LFS has hard water with a high pH, that may be worse than doing nothing at all. Bogwood, OTOH, would acidify and soften your water gradually. Get it a couple of weeks in advance of the fish so you can have it pre-soaked and ready to go in when they do.