Hello Nancy.  Thank you for using Ask Extension.  According to the American College of Allergy, Asthma, and Immunology, evergreen allergies are fairly uncommon.  It’s more likely that the symptoms stem from the tiny mold spores, dust or pollen housed on the trees or from terpenes (chemical compounds) responsible for the tree fragrance.  The selection of allergen-reducing plants for the yard may only have a limited protective impact on your son, since wind-blown pollen is the main allergen when pollen triggers allergies, and will thus blow through the yard regardless of the plantings within it. 

Arborvitae produces both male and female flowers on the same plant and the pollen is shed over a number of weeks in the spring. You can use female (less pollen) selections which won’t produce pollen at all.  Many of the commonly-grown conifers are monoecious, so would have pollen present: Falsecypress (Chamaecyparis), Japenese Cedar (Cryptomeria), Arborvitae (Thuga), Hemlock (Tsuga), and Spruce(Picea). 

From my readings, if you have adequate space and conditions, the Leland Cypress, Eastern Redcedar (Juniperus virginiana), Rocky Mountain Juniper (Juniperus scopulorum), Chinese Juniper(Juniperus chinensis), yews such as Taxus bachata and Taxus cuspidata, White Spruce (pica glaucoma), Eastern Hemlock (AtsugiCanadensis), and numerous Holly (ilex)varieties.  You might be able to trim the taller growers to size by lightly trimming their growth once they approach your limit.

https://www2.conifersociety.org/    This website has information that may help you further.  And also: https://www2.conifersociety.org/.      

You will need to check with local suppliers for what is available in your area.  Sizes and prices will vary.  It will take some homework, but you should be able to find some varieties that will work for you.  Enjoy the process and good luck with your son’s allergies.