Greek numbering

You can create a Greek equivalent by taking the code of e.g. \alph from the file latex.ltx and modify it to get what you want. It also requires a slight modification to the subequations environment from amsmath.

\documentclass[11pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}

\makeatletter
\newcommand*{\greek}[1]{%
  \expandafter\@greek\csname c@#1\endcsname
}
\newcommand*{\@greek}[1]{%
  $\ifcase#1\or\alpha\or\beta\or\gamma\or\delta\or\varepsilon
    \or\zeta\or\eta\or\theta\or\iota\or\kappa\or\lambda
    \or\mu\or\nu\or\xi\or o\or\pi\or\varrho\or\sigma
    \or\tau\or\upsilon\or\phi\or\chi\or\psi\or\omega
    \else\@ctrerr\fi$
}
\renewenvironment{subequations}{%
  \refstepcounter{equation}%
  \protected@edef\theparentequation{\theequation}%
  \setcounter{parentequation}{\value{equation}}%
  \setcounter{equation}{0}%
  \def\theequation{\theparentequation\greek{equation}}%
  \ignorespaces
}{%
  \setcounter{equation}{\value{parentequation}}%
  \ignorespacesafterend
}
\makeatother

\begin{document}
  \begin{subequations}
    \begin{align}
      (a+b)^2 &= a^2+2ab+b^2 \\
      (a-b)^2 &= a^2-2ab+b^2 \\
      (a+b)(a-b) &= a^2-b^2
    \end{align}
  \end{subequations}
\end{document}

You mentioned that you only want to modify some equations. The above introduced approach is a general modification. So you might have to do some adjustment on your own. At least you have Greek letters as enumeration symbols which also could be used at other places.

Taking inspiration from T.D.'s excellent answer, I wrote a small package to add extra counter output types. As well as greek, it defines binary, hexadecimal, and "First, Second, Third...".

• morenum.sty on github
• moreenum on CTAN

You can use the \greeknumeral or \Greeknumeral from the babel package. I am not sure how well they will play within a maths environment, but you can read the source for some inspiration.