Numbering proofs of theorem

Use amsthm and its proof environment that accepts an optional argument for setting a nonstandard label.

documentclass{article}
usepackage{amsthm}

newtheorem{theorem}{Theorem}

begin{document}

begin{theorem}
This is a big statement that deserves two proofs.
end{theorem}

begin{proof}[proofname 1]
This is the first proof.
end{proof}

begin{proof}[proofname 2]
This is the second proof.
end{proof}

begin{theorem}
This is a normal statement with a single proof.
end{theorem}

begin{proof}
Exercise for the reader.
end{proof}

end{document}

You can also type begin{proof}[Proof 1], of course. Using proofname automaticall adapts to the language if babel is used.

If you, for some reasons, want to automatize the numbering, you can set up a counter that's reset when theorem is stepped up.

documentclass{article}
usepackage{amsthm}

newtheorem{theorem}{Theorem}
newcounter{proofs}[theorem]
renewcommand{theproofs}{arabic{proofs}}

newenvironment{numproof}
  {stepcounter{proofs}begin{proof}[proofname theproofs]}
  {end{proof}}

begin{document}

begin{theorem}
This is a big statement that deserves two proofs.
end{theorem}

begin{numproof}
This is the first proof.
end{numproof}

begin{numproof}
This is the second proof.
end{numproof}

begin{theorem}
This is another big statement with two proofs.
end{theorem}

begin{numproof}
This is the first proof.
end{numproof}

begin{numproof}
This is the second proof.
end{numproof}

end{document}