General:
* Liquid
* Fluid
* Watery
* Thin
* Loose
* Soft
Specific to food:
* Saucy
* Gooey
* Slimy
* Mushy
* Melted
Specific to a nose:
* Stuffy
* Congested
* Drippy
* Sniffly
Other:
* Flowing
* Streaming
* Trickling
The best substitute for "runny" will depend on the specific situation. For example, you might use "watery" to describe a runny soup, "drippy" to describe a runny nose, and "gooey" to describe a runny cheese sauce.