Plant flowers that like some shade, such as foxgloves, geraniums, daffodils, azaleas and violets. These are all shade-loving plants that will thrive in the gentle glow of the morning sun but will wither and die in the intense afternoon heat.
Remove or prune any trees that are located on the east side of the yard. It is vital that the morning sun is not restricted in any way, and a large or particularly dense tree may do just that. If you don't want to cut it down completely, then simply prune it back hard each year.
Plant trees on the north or west side of the yard. These will provide some much-needed shade from the afternoon sun in the summer months. Having trees close to the house can even reduce your reliance on air conditioning in the summer, so it also makes good financial sense to plant some.
Plant shade-loving plants under any large bushes or trees that provide a shady spot. Hostas, for example, love dappled light, so they can be planted underneath trees. Some roses can also be planted in shady areas or areas that get only very little sunlight each day.
Install a bird bath or water feature of some kind in the area that receives morning sun. Full sun on water can cause algae to grow rapidly, but this is not a problem for water that only sees the morning sun. Evaporation will be less extreme as well.