I ride those greenway trails also and I have a pretty good idea about where you may be talking about on the Salado Greenway.
There is a stretch that runs between S.S. Lions park on the southeast side and in between Commanche park that has about three bad spots with that thin layer of silt.
To be honest with you, I don't think there is a tire made that can prevent you fron slipping and sliding on that slime since it is purely wet clay and even a knobby tire will just fill with the clay and be like riding a slick and your then back to square one.
Best advise is do as I do and avoid it until it dries out enough to be able to ride over it, which may take a day or two of dry weather.
It would help if the maintainance people who are suppossed to attend to the trails would be a little faster at keeping the trail clean since it doesn't go away once it is dry and just sits there waiting for the next rain to turn slick again.
Where do you ride?