It's a little hard to tell from your image, is the problem that the emitting object is very complex?
If this is the case then the way we tackle this usually is to assign a material with some self illumination to it, then model a low poly mesh around the object to aproximate the volume and apply a corona lightMtl to this.
Set the lightMtl to invisable, not to obscure other lights and adjust intensity to the desired level.
Pretty much what I would advise.
A short note about the reply above - using self illumination will probably make Corona slower since it's solving only by GI samples then. Using a LightMtl is always the better option as this will use optimizations like lights do. So try to avoid self-illumination in materials if possible and use LightMtl whenever possible.
Any excessive self-illumination will be cut off by Max Sample Intensity parameter, so it should not be a problem.
I would vote for:
The simplest solution:
-Forgetting about the small LED light sources, unless they are absolutely necessary (if they, or their shape, are visible through the diffusor)
-Just modelling the diffusor and applying a self-illuminated material to it (this will be the directly visible part that does not cast any light into the scene)
-Then placing a simplified mesh with LightMtl below the diffusor, and unchecking visible directly, visible in reflections, visible in refractions, occlude other lights (this will be the invisible light source which does cast light into the scene)
The LightMtl could be as well replaced with a RaySwitchMtl (so that it is visible directly, but nowhere else).
The slightly more complex solution:
-Create a lot of LED objects with light mtl with emit light off, or self-illuminated CoronaMtl, or some kind of RaySwitchMtl
-Create the diffusor below them, with any relevant material (e.g. refraction, translucency)
-Create the invisible light emitter like in the 1st option
