Díaz has nothing to do with día as you can see at http://www.ancestry.com/name-origin?surname=diaz
Also, I don't understand all this talk about slave owners in relation to the surname Diesel. There were thousands upon thousands of people from Europe and Asia who emigrated to South America from Europe and Asia in the last couple of centuries, e.g., Sabatini and Messi from Italy, Pinochet and Betancourt from France, Fujimura and Fujimori from Japan, etc. I have three friends named Ivancic (Serbo-Croatian), Baibich (Jewish) and Malouf (Arabic) who were born in either Argentina or Brazil. Diesel was simply one of these migrants.
And for an example of a Spanish surname ending in -el, see http://en.wikipedia.org/wiki/Chico_Carrasquel