Baking – a substitute for spry

The most accurate substitution would simply be rum extract. It is concentrated rum with a huge kick of flavor, and much less alcohol. A little goes a long way.

If you're going to stick with a strong liquor my first choice would be a bourbon, it's a similarly "sweet" liquor that tastes good in baking. Another good option would be cachaça.

If you're avoiding liquor, then you may be able to use vanilla extract. Non-alcoholic varieties are available. According to Ochef you can also use molasses thinned with pineapple juice.

The rum is used simply for flavor.

It depends what the recipe is, but I've successfully replaced brandy with orange juice or apple juice in the past. It's not a direct replacement for the flavour, of course, but gives a similar strength of flavour, if you see what I mean.