You could always draw in centerlines at the spline ends and then make your handles collinear. I'm going off memory here so it might be another relation, I've used centerlines to help control spline handles before.
Steve's on the right track with the centerlines or construction lines.
I would place an On Plane constraint between the end points of the spline and the face of the body. Sketch construction lines from the end points of the spline and apply a perpendicular constraint between the construction line and the face. Finally apply a Tangent constraint between the spline and the construction line.
You may have to use the spline handle to drag the spline to approximate the tangent condition before applying the constraint.
I'm assuming that you are setting up some guide curves for a loft so you may need to make the spline coincedent to an edge on the body face; I get an errror message if the guide curve doesn't start and stop on an edge.
There you go - nice detailed answer. First time answering through my Dolphin Broswer on my Droid RAZR...
Here's a picture (If I can the darn thing to load) - Centerline is Perendicular to the highlighted face and then Collinear to the spline handle - this is just to show an example of a way to use a centerline to help guide the spline handle or spline itself.
Thanks so much to both you and Steve for the quick, detailed answers. It turned out even easier, because the bodies were both cylinders so there were already temporary axes in the correct orientation. I just had to constrain the spline tangent to the axes. I was never given a colinear option, which is what I had been looking for and why I was stuck. Not sure why I didn't think of tangent - seems obvious now.