The original Monte Carlo station (opened in 1868) was immediately below the Casino, allowing it was said a quick getaway after a disastrous night at the tables. This was replaced by a rather functional SNCF affair in 1958 on the other side of the harbour, a few streets inland - the rest of the line being diverted through tunnel. This was in turn replaced by a wholly tunnelled line and station further inland in 1999. The lift-shaft to the tunnelled walkway to the current station is roughly where the 1958 station was, but the whole area has been comprehensively redeveloped. There is no trace of the 1868 station site either, being engulfed by various developments. Near to the French border on both sides of the Principality you can see traces of the old formation from the current line just before you plunge into the tunnel.
According to Wikipedia there were originally two stations in the principality. Monte Carlo for the Casino, and Monaco further west, about 1.5km apart. The first bypass tunnel, avoiding Monte Carlo, was completed in 1958 but the map on the Wiki page suggest that station remained open in some way until 1965. At some point the alignment was abandoned and reused for a new road, Boulevard du Larvotto, passing through the line's short tunnels and over new viaducts in the centre past the casino and presumably right through the old station site, and to the east of the harbour. You can follow it on Google Streetview. Further west, Monaco station remained open until the second bypass tunnel and new underground station were finished in 1999. Some of that alignment particularly around the old Monaco station itself has been redeveloped already while other parts further west remain unused.
The wikipedia page (refer to map image)
https://en.wikipedia.org/wiki/Rail_transport_in_Monaco
Here's a picture near the Casino looking east
https://primotipo.files.wordpress.com/2015/09/monaco-1958.png
...taken in 1960 by the particular car captured according to the blog post the pic is from, which is a hardcore racing history site so is quite likely to be correct. That is after 1958 when the tunnel had supposed to have opened so that suggests the 'Monte Carlo loop' may have lasted longer, as suggested by the wiki map.
Here's the same site on Boulevard du Larvotto today from Streetview
Here is a picture of the old Monte Carlo station itself looking west, again claimed from 1960
http://trains-worldexpresses.com/600/605a-08m.JPG
Elsewhere the new structures along Boulevard du Larvotto look later than the 1958 tunnel or thereabouts so that again suggests the Monte Carlo alignment segment may have remained at least in place if not in use for a good while before the road was built, but the whole principality is a constant building site so its possible they have been replaced or reconfigured a number of times since original construction.
For instance:
