Aphids aren't eggs, do they have legs and antennae? Ants tending them would imply they were aphids. If there aren't many you could crush them or blast them with a jet spray of water a few times.

4' is a small shrub, you want something that will grow bigger than the space? Considerations of scale aside, broadleaf evergreen shrubs for south walls include

Abelia
Azara
Acca (Feijoa)
Ceanothus
Choisya
Cistus
Escallonia
Euonymus japonicus
Hebe
Pittosporum tobira

Hi Ron - thanks for the reply! I'll definitely check out your shrub suggestions! And the green things are just clumped onto the tree branch and they aren't moving. I can't see any antennae or legs, but they're the same color and size as aphids. I'm going to blast them w/the hose and see how that goes.

Might happen to be the eggs of a beneficial insect, maybe better to keep an eye on them, do nothing until- and only if you see pest insects appearing after the eggs start opening.

HELP, I have the same ugly light green colored eggs on the underside of my flowering crabapple tree. I don't care if they are beneficial or not. Please tell me what I could use to kill them before they infect everything on my balcony. Thanks in advance guy's. This is so gross.