How can I use align environment in conjuction with iopart.cls class?

Put following two lines just before \usepackage{amsmath}

\expandafter\let\csname equation*\endcsname\relax

\expandafter\let\csname endequation*\endcsname\relax

Now even though you have iopart.cls as class file chosen, you would still be able to use amsmath package without any error. It will go like..

\documentclass[12pt]{iopart}

\usepackage{iopams}

\expandafter\let\csname equation*\endcsname\relax

\expandafter\let\csname endequation*\endcsname\relax

\usepackage{amsmath}

It's very unfortunate that the iopart class doesn't want amsmath, which is a robust package, very useful for mathematical writing.

Having eqnarray only for formatting multiline displays is a big hindrance, but there seems to be nothing else to do. However, the iopart version of eqnarray at least corrects the worst error in the spacing of the relation symbol used for the alignment.