I came across this question as I was trying to imitate a password input as well, but overlaying another div with •s wasn't an option for me, since I wanted it to work without JavaScript, too.
Then there's text-security: disc, but there isn't enough support for that as of this moment.
So what I've done is create a font on FontStruct in which all Latin characters (including the diacritic ones) look like a •.
Here is a link to the file on my Dropbox.
When using this, just add this in your css file
@font-face {
font-family: 'password';
src: url('../font/password.woff2') format('woff2'),
url('../font/password.woff') format('woff'),
url('../font/password.ttf') format('truetype');
font-weight: normal;
font-style: normal;
}
Then to use it, simply apply font-family: 'password' to your element.
P.S. If the Dropbox link is down and you happen to have it downloaded, feel free to replace the link. Otherwise just give this answer a comment