Generate new points on polyline from existing points on polyline

I have a polyline that represents the thalweg of a river. I have points snapped to that polyline, which represent locations where I've collected data. I am looking for a Python tool that will allow me to generate two points: one point located a set distance upstream of my original point on the thalweg and a second point located a set distance downstream from my original point on the thalweg. A Python analog to DistanceAlongCurve in ICurve.QueryPointAndDistance would be great, but I can't find a tool that will do the trick.

I am using ArcGIS 10.0 with an ArcInfo license. Thanks!