I know a handful of cities whose denizens can be called "city+er", e.g. Londoner. But is this construction still in active use today and can new demonyms be formed by it?
Sure. It is perfectly productive, with the fine print indicated in John Lawler’s comment, i.e., limited applicability: not every place name will sit happily with the -er suffix. Many will, however; treat yourself to some unexpected examples in this list .
But I have not yet quite proved my thesis. A nice evidence of productiveness of the suffix in English is its applicability to fictional place names. Thus we have a
Bucklander (example), a
Hogsmeader (example), an
Ankh-Morporker (example), etc.