Does the Thorncaster Sliver's ability damage have to be assigned before or after blockers are declared?
As with most abilities, you choose the targets as part of placing the ability on the stack. The damage is assigned and resolves before any blockers are declared.

I will cite ikegami's answer from another question related to Thorncaster Sliver.

https://boardgames.stackexchange.com/a/12644/3128


  Here's what happens:
  
  
  You attack with five slivers. Five instances of Thorncaster Sliver's ability triggers
  You place the abilities on the stack in the order of your choice: (Best order used)
  
  
  You place PS#1's ability on the stack targeting the 2/2
  You place PS#2's ability on the stack targeting the 2/2
  You place TS's ability on the stack targeting the Blood Artist
  You place MS#1's ability on the stack targeting your opponent
  You place MS#2's ability on the stack targeting your opponent
  
  MS#2's ability resolves:
  
  
  Deal one damage to your opponent.
  
  MS#1's ability resolves:
  
  
  Deal one damage to your opponent.
  
  TS's ability resolves:
  
  
  Deal one damage to the Blood Artist
  
  The Blood Artist dies. Blood Artist's ability triggers.
  Your opponent places Blood Artist's ability on the stack targeting you.
  Blood Artist's ability resolves:
  
  
  You lose one life.
  Your opponent gains one life.
  
  PS#2's ability resolves:
  
  
  Deal one damage to the 2/2.
  
  PS#2's ability resolves:
  
  
  Deal one damage to the 2/2.
  
  The 2/2 dies.
  [Move on the Declare Blockers]
  


The emphasis is mine.