This question has two components: firstly, can a character with Assassin levels trigger their Death Attack (after the three rounds of study, of course) by making a Coup De Grace against the helpless opponent they studied? Secondly, can I make a coup de grace and/or death attack with a melee touch spell such as Shocking Grasp, Vampiric Touch or Poison?
Let's check the definitions.
Death attack (emphasis mine):
Complete Mage, Spell Compendium and Rules Compendium have no additional information on the subject.
Spellwarp Sniper 5 gains the ability to coup the grace with a ray spell that deals hit point damage.
This ability still doesn't allow to trigger Death Attack.
I would always answer this question "Yes".
According to the 3.5 SRD "Touching an opponent with a touch spell is considered to be an armed attack", and it certainly is melee.
Since a touch spell that causes damage is basically the same as a natural weapon, or a trained unarmed strike, both of which can be used to coup de grace, I'm not sure why the answer would ever be "no". If an unarmed strike can coup de grace, Shocking Grasp can certainly coup de grace.
Addressing the second part, I'd say that yes, you can coup de grace with a touch spell. I'm basing this off the following, from Combat Actions:
So, an attack with a touch spell is considered a melee attack, and is considered an armed attack. An armed attack is generally one made with a weapon. Coup de grace requires you use "a melee weapon". This strongly points towards being able to use a touch attack for a coup de grace.
Further, you can score critical hits and sneak attack damage on this type of attack, and can deliver touch spells with a punch, so every ounce of "in game" sense tells us you should be able to deliver a coup de grace this way.
One thing you didn't bring up: In most cases you'd have to have touch spell already prepped, so you could simply deliver it with a regular unarmed attack -- which might bypass some of this discussion.
Note on the RAW
I think the wording of coup de grace would technically let you use a dagger to perform a coup de grace from across the room. They really meant to restrict it to a "melee attack" rather than a "melee weapon", and if they'd worded it differently this whole question would have been easier to answer. :)
When the RAW aren't abundantly clear, I tend to fall back on visualization and my own sense of how things work in the world I'm running. The sections quoted by other answers here can certainly be interpreted as implied. However, when I envision a coup de grace with a dagger, I can understand how anyone could work out how to inflict a mortal wound against a helpless foe. That's harder to envision when using shocking grasp, chill touch, etc. without some serious anatomy knowledge. I would probably find my myself ruling on a case-by-case basis based on the spell effects and the character's skills.