Smoothing sparsely sampled signal
It seems to me that curve fitting would be the most promising method for your problem, but instead of trying some random model functions (polynomials, wavelets, ...) that probably don't have anything to do with the physical reality of the thing you are measuring you should use a model function that you can expect to do well, i.e. choose one that is backed by a theoretical model that describes your setup. 

As long as you don't tell what you are actually measuring you can't expect much more help here.