Is it possible to replace the sugar in Tapioca Meringue pudding with stevia?
In meringues sugar is important mainly for the final texture, much more so than for it's sweetening effect. 
Since Stevia is much sweeter than sugar, one would have to use far less in order to not ruin the taste.  ("collectively, they give stevia 100 to 300 times the sweetness of sucrose")
Yet even taking half as much normal sugar than the recipe calls for will result in a vastly different meringue (not as stiff and less stable over time). The same problem stands for other  sweeteners. 

I'd therefore try using a sugar alcohol that has comparable (or even lower) sweetness to sucrose, so you can use a similar weight of material and get the texture just right (after some experimentation perhaps). Then, if that ends up not being sweet enough, you can still add a tiny bit of stevia solely for sweetening. 

For meringue, the following properties seem especially important in sugar substitutes: 


similar hygroscopicity to household sugar
less or comparably sweet than household sugar (so that bulk quantities may be used without ruining the taste)
low laxativity (because rather high amounts might be consumed) 


Have a look at this list. 
Erythritol won't work well because it is not hygroscopic enough, all the other options have a laxative effect.

I'd therefore advise against using sugar substitutes if you  don't absolutely need to. 

If you want to just sweeten the pudding itself separately with stevia, go for it. Pudding gets it's texture mostly from starch (or gelatin) so the lack of sugar won't have a detrimental (or even positive, in the case of starch) effect on texture.  

Having said all that; it seems possible to get decent meringue without adding any sugar at all if you get the technique just right otherwise (and add cream of tartar and perhaps starch). See also this answer. Personally, I've been dissatisfied whenever I used less than a ratio of 1/3 of sugar to egg whites and find 1/2 best for swiss meringue.