Here is a pipeline for miRNA detection from Solid color-space reads:

• http://bioinformatics.oxfordjournals.org/content/early/2011/12/09/bioinformatics.btr686.abstract
• http://personalpages.manchester.ac.uk/staff/antonio.marco/seqtrimmap.html

Here is another one that provides a web interface:

• http://nar.oxfordjournals.org/content/37/suppl_2/W68.abstract
• http://bioinfo2.ugr.es/miRanalyzer/miRanalyzer.php

There are likely to be many others out there...

Public dataset will typically be posted on the NCBI databases GEO and/or SRA:

http://www.ncbi.nlm.nih.gov/geo/ http://www.ncbi.nlm.nih.gov/sra

You can also select a publication that you like (or that you'd like to reproduce) and use their data. In most cases, the paper provides the link and the accession number to the public database. For all microRNA-related information, miRBase is a good starting point: http://www.mirbase.org/