If you intend to reconstruct a tree for the miRNA sequences themselves, then you can use any suitable method for nuctleotide sequences. E.g. you can use maximum likelihood or bayesian reconstruction. Perhaps MrBayes is the most popular software nowadays. Pay attention that you have a high quality alignment.
If you intend to make a tree based of the presence or absence of certain miRNA genes, it is also possible, but more unconventional, and it requires more deep knowledge of the methodologies.
yes I also agree with what Csaba has suggested...since miRNAs are as good as other gene sequences...so you can use any method suitable for analysis of nucleotide sequences for phylogeny...but as mentioned above there are several methods ...and they are based on certain assumptions...if you are clear about these things ..it will easy to use the appropriate method for your analysis......
but still I can suggest you to consider..one mmore option....if you are planning to use precursor miRNAs for this analysis.....such precursor molecules ..show high degree of secondary structure conservation across diverse organism....so you can use this information also for arriving at phylogenetic relationships...or evolutionary mechanisms operating on such sequences....go through some papers on this kind of analysis on RNA sequences...
Maximum likelihood and Bayesian Estimation is a superior method to go about. but also considering the Codon substitution models you choose and the complexities you increase in the system. In general F91 and K80 models can get you the basic snapshot. If using PAML go for Codeml and select model-1/2. I think you get the you the snapshot atleast. But still we need a deeper understanding into the best substitution model which will define trees.
Try searching some papers. I have not been through much of miRNA evolutionary studies. Try contacting Dr T.S. Vasulu in ISI, Kolkata
Step1: MSA of your sequences of interest (pri-, pre- or mi-RNA). This information can be easily obtained from miRBase (e.g., http://www.mirbase.org/cgi-bin/mirna_summary.pl?fam=MIPF0000007).
Step2: Import the aligned profile into a software (e.g., http://www.megasoftware.net/mega4/features.html). MEGA4 can also be used to perform multiple sequence alignment.