In the documentation for dist function in R there\'s the following words :
method the distance measure to be used. This must be one of \"euclidean\", \"maximum\", \
You can't; dist()
only knows how to compute certain distances. There are a good number of other distance/dissimilarity coefficients available in R packages via CRAN (including vegan, analogue and the proxy package, amongst many others.)
The latter, proxy, may be particularly suited to your needs. Not only does it have a large number of pre-specified coefficients, it provides a framework for specifying your own distance function that is then called from compiled code so is reasonably fast.