There are two separate issues with this question.
One is suppressing/negating, the other is dispelling.
Remember that both spells are range: touch, and target an object.
If you have an active daylight spell, then it will suppress a deeper darkness spell in the overlapping area, but the darkness will still be there if you move away.
To actually dispel the deeper darkness, you need to cast daylight on the same object (by touching it). Also, note that a bard, sorcerer, or wizard will need to heighten daylight to level 3, since the spell description says it will dispel any darkness spell of equal or lower level. Deeper darkness is a level 3 spell. (A level 2 daylight will still suppress, just not dispel.)
-Hyp.