There aren't many who are offering AOLserver+PostgreSQL hosting, and those seem to be targetting "serious" users, i.e. those who are developing and intend to host a commercial service.
When I first ported the bboard module to Postgres, I ran a demo on an old Pentium 200 hooked up to my home DSL line. It was enough to attract the curious and played a fairly large role in the establishment of the OpenACS project.
The current openacs.org site would run quite nicely on the same set-up, other than downloads where the relatively low bandwidth (256kbs up the line in my case) would be a pain. But for neighborhood community sites, small non-profits, etc a DSL line would work quite well. Mine's very reliable.
Roberto runs his site on an old P166 or something like that. It runs on University of Utah's network connection and that's a luxury, but the box itself is hardly an expensive one.
A step-up is co-location with a local ISP. My main OpenACS-backed site sits at a local ISP and costs me $100/month. That's not really all that bad.
So I guess the answer is that no, there's not much available in the way of low-end AOLserver+PostgreSQL hosting but that it's not really all that expensive to roll your own, either.