Is it okay for a married couple to use condoms if one of the partners has an illness that can be transmitted sexually?
No. Condoms cannot be used in such a situation and, in any case, do not entirely protect the uninfected spouse. If one spouse has a sexually-transmittable disease, the couple may refrain from marital relations. If the illness is cured, relations may resume; but if the illness is incurable, the couple may have to live a life of celibate chastity. While this is a very difficult situation indeed, such a couple could especially entrust their marriage to the Holy Family and take Mary and Joseph as models of celibate and chaste spouses.
For more information and assistance in such a situation, I recommend contacting a Catholic marriage counselor. Referrals can be obtained through CatholicTherapists.com and the Pastoral Solutions Institute.