The darkness spell description states:
Magical darkness spreads from a point you choose within range to fill a 15-foot-radius sphere for the duration. The darkness spreads around corners. A creature with darkvision can’t see through this darkness, and nonmagical light can’t illuminate it.
If the point you choose is on an object you are holding or one that isn’t being worn or carried, the darkness emanates from the object and moves with it. Completely covering the source of the darkness with an opaque object, such as a bowl or a helm, blocks the darkness.
If any of this spell’s area overlaps with an area of light created by a spell of 2nd level or lower, the spell that created the light is dispelled.
The darkness spell doesn't mention anything about creatures inside being immune to radiant damage. It makes sense to me that this would be the case, similar to how creatures inside magical silence are immune to thunder damage, although the silence spell specifically states this.
On the other hand, the PHB description of radiant damage:
Radiant. Radiant damage, dealt by a cleric’s flame strike spell or an angel’s smiting weapon, sears the flesh like fire and overloads the spirit with power.
It doesn't actually mention light being involved, but it seems implied by the name "radiant". According to Dictionary.com, the definition of radiant is:
emitting rays of light; shining; bright
My thoughts are that radiant damage is dealt by very intense light, and since light, except that produced by spells of 3rd level or higher, can't penetrate magical darkness, creatures inside of magical darkness are immune to radiant damage. If the radiant damage is produced by a spell of 3rd level or higher, it penetrates the darkness and deals damage as normal. Spells of 2nd level or lower are dispelled and do nothing.
Does radiant damage work in magical darkness?