How to make a toilet seat hinge more stiff?
If you're open to buying a new toilet seat you can find seats with stiff hinges such as this:

EZ Close seat

Random example, never used above product...

With little kids in the house, I've picked up a few of these type of seat from a local home store.  They are marketed as "Slam free", "slow close", "quiet close" and similar.  The hinge provides enough resistance so the seat will eventually slide to the close position, but it will not slam or start to fall by itself.

This might not be the cheapest answer, but my seats were due for replacement anyway, so it was a good option for me.