Before you buy dormant oil you might want to examine the health of the trees in general. Were they planted in the landscape or did they grow there naturally? If they were planted, they may be too deep in the ground
. If the root flare is buried
this kind of smothers the tree and the aphids are a sign that the tree is in distress. The aphids are opportunistic, looking for the ailing plant.
How is the drainage around the trees, see how they are planted, and was any chemical fertilizer or product used around them? For example, if someone used one of the Scott's turf products near a tree that will kill trees. In an organic program there is no place for those big-name chemical fertilizers because they do a lot of damage to the soil and microorganisms and leave things out of balance.
I suggest you take some time and read through or listen to the videos in the Organic Guides
(the link is found in the middle of the DirtDoctor.com home page). Look at bed prep, rose planting, sick tree treatment, etc. Get a handle on how this program works - it isn't just that we can name one non-chemical solution to the problem of aphids, it is a mindset that allows you to look at your yard holistically and know that if your lawn and your flower beds and your rough areas all have good biological diversity in the soil, the plants in those areas will be much healthier than in a chemical program.