I think most phylogeny computation programs (paup*, mrbayes, etc) tend to be run outside of R using nexus files, while R packages are used more for analyzing the trees and plotting (ggtree, ape, etc).

For literature searches, you probably need to define the type of interaction between your ncRNA and coding RNA in the search.  If I search pubmed for "non-coding RNA coevolution" and sort by relevance, there are mostly  RNA-RNA or direct RNA-protein interaction results.  Do you have evidence of your ncRNA interact with the protein coding RNA directly?  The only coevolution studies I've heard discussed are host-virus interactions.