Given the absence of anything that looks like an alternative to the comparative method (and internal reconstruction) in the historical linguistics literature, I think we can safely say that there is no alternative.
The method of mass (or multilateral) comparison is heavily critiqued, but whether one would subscribe to its use or not, it would not pose an alternative to the comparative method. If we take the comparative method as a way of i) establishing genetic relatedness between languages, ii) identifying systematic sound correspondences between them, in order to iii) ultimately arrive at a reconstructed proto-language, then multilateral comparison concerns itself only with the first step.
For example, Greenberg (1996: 131–132):
It seems to be
widely supposed that multilateral comparison and the
comparative-historical method are in some way contradictory. This is
perhaps most starkly stated by Nichols (1990:477, n. 1) as follows:
"Greenberg (1987) makes it clear that he believes such grouping
cannot be reached by the standard comparative method; a wholly
different method, mass comparison, is required." Where I supposedly
said this is not specified. In fact, just the opposite is stated: "...
my remarks are not intended as an attack on the validity of
comparative linguistics or on the importance of undertaking
reconstruction. Rather, the discussion is meant constructively as a
way of taking first steps where the comparative method has not been
applied for want of an assured basis in genetic classification" (LIA,
I said much the same thing in regard to the relationship between
the two much earlier (1957:44), namely, that the methods outlined
there did not conflict in any fashion with the traditional
comparative method and that they might be viewed as the first step in
the method itself, for we cannot begin systematic reconstruction until
we know which languages to compare. Whether classification by
multilateral comparison is to be viewed as a necessary preliminary
step in order to define valid genetic units without which comparative
linguistics cannot proceed or as the first step in the method itself -
an alternative which seems more natural - is a matter of definition.
The heart of the dispute then seems to be whether a classification of genetically related languages can be proven by way of multilateral comparison, or whether the relatedness can only be established by identifying systematic sound correspondences and/or a reconstructed proto-langauge. Either way, mass comparison cannot be counted as a full alternative to the comparative method, since it does not address the reconstruction of proto-languages.