I have a steep tree and grass covered back yard where rain water flows down during storms. This exits through the garage but is causing soil erosion. I too would like to know what sort of professional to consult about a diy drainage plan.
It depends on your own expertise. Landscape architects specialize in designing outdoor spaces including storm water management. However they're not regulated equally well in all states and are a design professional so you may have to shop around a bit to find one you work well with. A good one can give you a complete plan that's going to be attractive and not lower the value of your home. They may also have existing relationships with reputable contractors if the work needed is beyond you.
Civil engineers are experts in drainage, and they're tightly regulated everywhere. They're the go to resource for technical questions about how much water to expect in the usual and worst cases and sizing drains, dry wells, etc. Don't expect detailed information on which plants prevent erosion and attract birds or if a giant gravel-filled trench will look ugly.
Basically it boils down to your own design sense and familiarity with the subject. A landscape architect can provide more hand holding, an engineer can provide more detailed answers to specific questions.
It is slightly alarming that your garage is involved though. The civil engineer is a safer bet if there's a possibility of the garage's stability being compromised.