So finally I got offered a satellite contract!
I've kept playing, ferrying tourists around Mun, rescuing Kerbals from Kerbin and Mun orbit but still not a single satellite contract in sight.
One thing made me wonder though: I didn't get as much contracts offered anymore as when I started out with my career. Mostly I only had 3 new contracts available at any given time. Cavscout74's mention of the AverageAvailableContracts number made me think that maybe the currently active contracts also play a role in this, and from them I had quite a few (mostly around 12 or so. Most of them generic contracts for achievements like planting a Flag on Mun or Duna, but some also from companies).
So eventually I decided to cut down on the number of active contracty by fulfilling some of them, _without_ immediately accepting another one upon completion, and all of a sudden I got 5 available contracts with my first satellite contract amongst them. (An equatorial orbit in westerly direction, so I had to design a new probe carrier rocket for that)
So I can conclude, that it seems that the number of running contracts also affects the number of new contracts you will get offered, and (at least it seems to me), that the few contracts you do get offered tend to be from the same type as contracts you already accepted or completed in the past, thus making new types of contracts more unlikely to get available.