who pays for the death penalty executions?

The state, i.e., the taxpayers.
The practice of the condemned person's giving the executioner at his
beheading a tip has gone out of style, but had its purpose; quite
painful if he bungles the job and needs a second whack.  Besides,
there wasn't much reason for the condemned to be parsimonious.

Depends where. In China, families of the deceased are ordered to pay
for the bullets. Moreover, there have been reports, that the state
sells prisoners' organs for transplants. And this is where we're going
to have the next Olympics...

Erik Baard and Rebecca Cooney, "China Executions Inc.", Village Voice,
May 2 - 8, 2001
<http://www.villagevoice.com/news/0118,baard,24344,1.html>

American University, Illegal Human Organ Trade from Executed Prisoners in China 
<http://www.american.edu/TED/prisonorgans.htm> 

 China's Social Changes Spur More Executions; Families Don't See the
Body, But They Pay for The Bullet
<http://www.tibet.ca/en/wtnarchive/1994/3/27_3.html> 

JULIAN GEARING, "From Our Correspondent: An Execution in Shigatse",
AsiaWeek, December 11, 2000
<http://www.asiaweek.com/asiaweek/foc/2000/12/11/>