1077 has answered and I concur with all of it. Just a comment from my personal experience, as I have the same issue.
Tap water here is 0 degrees dGH and kH, and pH 6.8-7.0. My tanks once set up slowly lower in pH, as 1077 explained its a natural biological thing, and when they get to where I want them (just above 6 is OK, I have all soft acidic water fish) I put about 2 tablespoons of dolomite in a nylon bag in the top filter chamber. For 10 years this kept the ph consistent 6.2 to 6.5 with the diurnal variation (I have heavily planted aquaria and a diurnal pH fluctuation is natural).
Dolomite is a limestone base gravel that aquarists use in marine tanks and sometimes African rift lake cichlid and livebearer tanks, since these all require harder, alkaline (basic) water. Use very little, and in something like a bag so you can add/remove it, as once it is mixed in the substrate (another method, not so good) it is difficult to remove. I understand coral chips and marble chips also work the same, but have not used those myself. A small bag of dolomite gravel is not expensive.
You can also raise GH by adding magnesium sulphate (pure Epsom Salts) to the water. I've used this previously and am experimenting with it in one of my tanks now actually [won't get into the why]. The only thing is that you need to work out the amount as it raises the GH quite suddenly, and keeps it there for at least a week; the partial water change dilutes it obviously, so it has to be replaced each water change. I think for your purposes the dolomite works better.
In my tanks, the dolomite alone in the filter of a 115g aquarium raises the GH by 20ppm and it is constant. The trick is finding the correct amount. Start with very little, 2 teaspoons for a 10g tank, in a small nylon bag in the filter if this is possible (your type of filter) or hang it next to the filter return. It takes a few days, so leave it for a week, measure the pH (and GH if you can) after a couple of days and then monitor it. Partial water changes will have little effect on dolomite treatment, since your tap water is higher in pH. In a few weeks you should see the pH stabilize. If it hasn't gone up at all after 3 weeks, add another tsp of dolomite. The change is gradual so no harm to the fish (procided you don't use too much of course).
Do not use pH adjusting chemicals, with no hardness they will act very quickly and fluctuating ph is very stressful on fish. Plus chemicals in general do not belong in fish tanks; some fish have a strong sensitivity to such things, but all fish do not benefit from chemicals.
With wild caught fish from SA or SE Asia hardness would be of very little importance, but many of the fish commonly available today are now commercially raised in tanks or outdoor ponds, and often in water closer to tap water in most areas (neutral to slightly alkaline, some GH and kH depending upon location). When fish lke neons that have ben commercially raised for years now are placed in what should be perfect water from their native habitat, they becomes stressed and can die from the shock or cumulative effect over time. I have wild caught cardinals and tank-raised cardinals, and it is not surprising that the tank-raised fish are having health problems whereas the wild are not; this is why i am now working on raising my GH every so slightly, so as not to jeopardize the wild fish (I have wild and tank-raised fish of several species together in the same aquaria) but assist the tank-raised. So far it seems to be improving.
Byron.