Can anyone suggest Paragon Paths that will help a character that is based on inflicting ongoing damage to their opponents?

A search for "ongoing" gives 127 PP entries. You could either sift through all of those, or narrow down your role/class selections a bit more a bit. What class is the character?

There isn't really a single class. I think the most "ongoing" damage is from Warlock's but not actualy from an ongoing damage application, mostly through sustained abilities.

I think Rogue and Fighter both get some "bleding" flavored powers. Sorceror might get a couple ongoing damage powers too. 

Page 78 of the "Player's Strategy Guide" has tips for building a character based on ongoing damage.

Cruel Cut Style

Prerequisite: Wis 13, any martial class
Benefit: You gain a benefit with any of the following powers you possess.
Cleave (fighter): If no other enemies are adjacent to the target when you hit the target with this exploit, the target takes ongoing damage equal to your Wisdom modifier (save ends).
Furious Smash (warlord): If your ally hits with the attack this exploit provides, the target takes ongoing damage equal to your Wisdom modifier (save ends).
Predator’s Strike (ranger): If your beast companion hits with this exploit against a creature granting combat advantage to it, instead of adding your Wisdom modifier to the damage roll, you can have the target take ongoing damage equal to your Wisdom modifier (save ends).
Riposte Strike (rogue): If you hit with the riposte this exploit grants, the target takes ongoing damage equal to your Wisdom modifier (save ends).

Might try this for at-will's to get ongoing.

On a side note, I used to play a rogue that was focused on doing high levels of ongoing damage with penalties vs the saves. It was alot of fun, but tough to do very often, since ongoing damage, at least for rogues, tends to come exclusively from daily powers and items.