limiting number of connections from specific host or by user

We are having a problem where we are running out of connections due to a
in-house tool that creates abnormal amount of connections due to fluctuating
loads that we cannot control.  Ideally, the tool could be re-written to take
into account for those situations, but due to its complexity we don't have the
time to do so.  I am trying to come up with a solution to block incoming
connections when they reach a certain hard limit.  Is there any way from
PostgreSQL user authentication or other methods to cap connection count by user
or by host?  I had considered creating a firewall rule after detecting a certain
amount of established connection from a particular host, but this seems very
inflexible as well.  Any ideas or suggestions appreciated.

Sincerely,
Kenji