Is there an effective alternative treatment for allergic rhinitis?  My
husband takes antihistamines, but they make him sleepy.  The
non-drowsy ones like Claritin don't work.

Although you didn't mention it, one of the most common drugs is
cetirizine, which is what I'm guessing your husband took and is making
him sleepy.  Although I'm not sure if it would disrupt the medicines
purpose, or whether the medicinal properties would last well until the
next night, your husband might consider just taking nightly bedtime
doses of the drug, so if he gets sleepy, he's going to bed anyway.  I
wouldn't do anything until you get an official answer, though, because
I'm no medical expert.

Hope this helps anyway.

While it is important to identify what your husband is allergic to,
there certainly are some rather generic alternatives that can be
helpful. These are intended as general comments, and not specific
medical advice:
1) Get a good HEPA air filter for your bedroom. You spend about 1/3 of
your life in bed, and reducing the allergic load while sleeping can
significantly improve symptoms.
2) Bioflavonoids such as quercetin and hesperidin methylchalcone can
decrease the hyper-reactivity of the mast cells and basophils which
release histamines and cytokines that cause the symptoms of allergic
rhinitis. Vitamin C may also be useful in this regard.