There are a couple of questions on SO regarding the pros and (mostly) cons of having SQL Server and IIS running on the same machine:
http://stackoverflow.com/questions/1401834/when-can-i-host-iis-and-sql-server-on-the-same-machine
These questions seem geared towards heavy-duty installations though and most of the concerns involve the memory demands of both servers.
However, if I am installing SQL Server Express, which can only utilise 1GB RAM, on a box with 2GB RAM then I presume memory will not be an issue, as SQL Server will gobble up the 1GB it can leaving the rest of the memory for IIS and other processes?
I appreciate the other concerns over CPU cycles, security & maintenance remain, but as this would be for an internal production monitoring system which will have a maximum of about 20 concurrent connections, these will not be a major concern.