Consulta MYSQL entre dos marcas de tiempo

Prueba:

SELECT * 
FROM eventList 
WHERE  `date` BETWEEN FROM_UNIXTIME(1364256001) AND FROM_UNIXTIME(1364342399)

O

SELECT * 
FROM eventList WHERE  `date` 
BETWEEN '2013-03-26 00:00:01' AND '2013-03-26 23:59:59'