Journal Papers
[2]
[1]

Conference Papers
[2]
[1]

Journal Papers
[C2]
[C1]

Conference Papers
[C2]
[C1]

documentclass{article}

usepackage{etoolbox}
usepackage[backend=bibtex,style=ieee,sorting=ydnt,defernumbers]{biblatex}

AtDataInput{%
  csnumgdef{entrycount:therefsection}{%
    csuse{entrycount:therefsection}+1}}

DeclareFieldFormat{labelnumber}{mkbibdesc{#1}}
newrobustcmd*{mkbibdesc}[1]{%
  numbernumexprcsuse{entrycount:therefsection}+1-#1relax}

addbibresource[label=journals]{my_publications.bib}
addbibresource[label=conferences]{my_publications.bib}

begin{document}

begin{refsection}[journals]
  nocite{journal1,journal2}
  printbibliography[prefixnumbers={J},title={Journal Papers}]
end{refsection}
begin{refsection}[conferences]
  nocite{conf1,conf2}
  printbibliography[prefixnumbers={C},title={Conference Papers}]
end{refsection}

end{document}

latex doc
bibtex doc1-blx
bibtex doc2-blx
latex doc
pdflatex doc