A common drug used in attempted suicides is sleeping tablets of various forms. Decades ago, when barbiturates were prescribed for sleep issues, it was possible to overdose on them. Modern sleeping tablets are not, by themselves, lethal, and taking a large dose as a suicide attempt is more likely to result in a long sleep and a trip to the hospital emergency department than death.
What does not appear high on the list of drug related deaths is barbiturates. Although a number of barbiturates are highly lethal, the reason they don't appear highly on the tables of drug related deaths is that they are now rarely prescribed, and extremely difficult to obtain without a prescription.