I have looked at the self-hosted web browser based IRC-clients Subway and Alice as I never seem to get an invite for IRCcloud.
The two alternatives I have found suffer from really bad bugs. They work for about an hour, and then it seems their communication with their backends just falls apart. Subway duplicates all open channels ever few hours and sometimes sporadically reloads. Alice has ridiculously long delays for delivering messages. Side-by-side with another client it can be up to 15 minutes (!) out of sync, and that will not do for an instant messaging client.
Are there any other alternatives I should take a look at? or services?
The desktop IRC clients for Linux simply does not cut it for me, and I like having a persistent connection that I can join from wherever.
In case someone stops by years later, The Lounge (website / source code), in its private mode (see the configuration docs), will do what the OP wanted :)
It is an actively-developed, official fork of Shout (mentioned in another answer here) now inactive, and is recommended by the author of Subway (mentioned by the OP).
The following clients are my favorites.
I hope this helps!
I would like to offer the suggestion of "Shout". I hope that that is helpful to someone who views this in the future. ;)
You can Try http://mibbit.com Its not a bouncer but it is a web based client.