If you use codemirror for the editing portion, you can use https://github.com/achengs/subpar to provide a subset of paredit in the browser.

Is there a parinfer package for emacs ?

Not that I know of, but adjust-parens is similar

Check the parinfer site, I'm pretty sure the implementation there runs on CodeMirror so it should be easy to get on your site if that's what you're using.

IIRC pareninfer is written in cljs, so porting it shouldn't be too hard.