There are a number ways of automatically generating texture coordinates, but I don't know of any easy way to do it that will give you coordinates without significant distortion or excessive discontinuities.
I would say that the easiest approach will be to write a small program that converts from your current model format to something more standard. I've done this in the past, and I've found the XNA .x format pretty easy to convert to. I think anything else you attempt will ultimately take longer and be more difficult than doing this and then using the tools available in a 3D modelling package.
If you're absolutely certain you don't want to do the conversion, then my advice is to aim for something simple, and accept that the results won't be great. One easy approach is a spherical projection - basically you assign the texture coordinates to vertices based on the "latitude" and "longitude" corresponding to a vector going from the centre of the model to the vertex.
Similarly easy, but often better for things like characters is to project all forward facing polygons to just their x and y coordinates, and similarly for the back facing polygons except that you offset them so the two sets are next to each other.
Going further you could try cylindrical projections also. Each of these projections will work well for certain kinds of shapes. But, generally they will be much worse than proper UV unwrappings like in Blender, etc.