How can I deal with indestructible shrouded slivers?
Depending on how far you want to go to tune your deck for this specific scenario you have a few options.  If dealing with this combo is more important then staying mono-green looking at a black splash will open up a lot of the cards ideal for this match up.

General advice, Exile and negative toughness effects will still remove indestructible creatures, and Edicts (sacrifice effects that target the other player) will get around shroud as well.

Assuming that we are staying mono-green, Some specific Cards:  


Perilous Vault will get around both by exiling everything, I recommend saving it to both play and activate in the same turn to avoid getting it destroyed   
All is Dust will act as a board wipe    
Ugin, the Spirit Dragon another board wipe  
Aligned Hedron Network can deal with the Hive Lord  
Arcane Lighthouse remove shroud  
Bonds of Mortality will remove the indestructible  
Sword of Kaldra will exile something it deals damage to, this could be used with a lure to force blocks  
Pithing Needle or Phyrexian Revoker naming Sliver Overlord will stop the activated abilities on the Commander.     
Song of the Dryads,Lignify on the Overlord can slow down searching up the combo.   
Jester's Cap can remove the problem cards from his Library  
Damping Matrix can shut down the activated abilities of the commander  
Bind can counter one activation of search to buy time  
Triumph of the Hordes would also be a good answer to just go over in a green deck  


Additionally you can look at some infect / wither for some creatures which will place -1/-1 counters which get around indestructible, or annihilator which will require sacrifice.