Re: How far from 90 degrees can a bowling pin move before it falls over?

i'm afraid you are going to have to experiment on that one as you will 
need to find out the centre of mass of the bowling pin.  The centre of 
mass will be on the axis of the pin but the height will depend on how top 
or bottom heavy the club is.

See page 8 of this guide to find out how to locate the centre of mass and 
to read up on falling over. 
 http://www.mastep.org.na/PhysSc/IGCSEPSc/Forces.pdf

Assuming the bowling pin is of uniform density then you could use 
cardboard cut to  a flat bowling pin shape to locate the height of the 
centre of mass. This would be easiest.

An object will topple when a line drawn from the centre of mass vertically 
downwards does not pass through its base.

The angle between the base of the pin and the ground when this happens 
will be

90 degrees – the angle for which the tangent equals (height of centre of 
mass (h)) divided by (radius of the base of the bowling pin(w))