Hello,
In my experience with working with autistic spectrum children, depressive symptoms can occur by biological and environmental factors. Therefore, psychopharmacological interventions may be needed depending on the severity of symptoms to stabilize your child's mood. You're correct in that side effects can be problematic, and if you were to take this option, I would consult your psychiatrist about the meds as well as appropriate dosage levels. My suggestion is to GRILL him/her with questions because I've noticed that in working with psychiatrists, some tend to write prescripts haphazardly or overmedicate.
The other option may be psychotherapy, and research has shown that individuals who combine meds and psychotherapy show greater improvement in mood than either intervention alone. Being that your child is Asperger's tells me he/she is higher functioning and most likely verbal, so your child could benefit from such modality.
Perhaps you can also encourage your child to get involved in more activities. Maybe enroll your child in groups with individuals of similar developmental level. Hobbies, family outings, visiting family/friends, and other fun "stuff"! Physical activity, for example, works very well to counter depression and my favorite to counter stress. The problem with depression is as the individual withdraws from their normal routines, it can perpetuate and increase the depression. They lose their contacts/friends, increasingly lose interest in activities they once found pleasurable, etc. Essentially, it can spiral down because they continue to lose "things" inside and outside of themselves. On a personal note, the challenge I have found with families of ASD children is how they offer their child a fulfilling life. Despite their delays, activities and fun are just as important for them as "typically developed" individuals.
Lastly, family support and communication is invaluable. Your child knowing he/she is supported and allowing them to communicate there feelings and difficulties matched by an empathic response can help elevate mood, decrease anxiety and other negative mood states. It will also help create a deeper relationship with your child. On another personal note, despite their relational difficulties, ASD children need positive relational experiences just as much as any other though they certainly approach it different than most others.
I hope my brief summary is helpful and I encourage you to continue to seek professional help in however you intercede for your child. GLTY and to your family!