Diffbot doesn't let you define custom tags. It however does allow you to assign relevant tags to all your images in an automated fashion.
Imagga and Clarifai are two products you might be interested in. They both allow you to define custom tags. Clarifai has a free plan that lets you tag 5000 images, a Standard plan that has Pay-As-You-Go pricing model, and an Enterprise plan (costing not available on their website). Imagga has 4 plans to offer that start from $14 per month.