Is intercourse in the Bathroom Permissible in Islam?

My brother, may Allah help you to do that which is good and make you satisfied with that which He has permitted you so that you will have no need for that which He has forbidden. What you have mentioned in your question may be answered by noting the following: 

• The modern kinds of washrooms in modern houses such as those in your country differ greatly from the places used in the past for relieving oneself, which were places where dirt, filth and impurities collected. Modern washrooms are not like that, rather they can be kept clean and there is no impurity in them. Therefore they are not like the places that people used for relieving themselves in the past, and there are obvious differences between them. On this basis, there is no real reason why one should not fulfil one's sexual desire in such places when necessary, in the manner that you mentioned.
• A man’s fulfilling his sexual desire with his wife may often happen as the result of stimulation, by looking or touching etc. Hence fulfilling his desire when it is provoked in such situations is a means of keeping himself chaste and lowering his gaze [from looking at other women]. This is what the Prophet (peace and blessings of Allah be upon him) taught us to do, according to the Hadith narrated by Muslim (1403) from Jabir (may Allah be pleased with him), who says that the Messenger of Allah (peace and blessings of Allah be upon him) saw a woman and he came to his wife Zaynab (may Allah be pleased with her), whilst she was tanning a skin and preparing it for dyeing, and he fulfilled his need. Then he went out to his companions and said: “Woman comes and goes in the shape of a devil [i.e., she causes temptation], so if any one of you sees a woman, let him go and have intercourse with his wife , for that will take away what he feels in his heart.” This was also narrated by Ahmad, 19403; Ibn Majah, 1853. Ibn Hibban narrated in his Sahih, 4171, that ‘Abdallah ibn Abu Awfa (may Allah be pleased with him) said: “The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘No woman fulfils all her duties towards Allah until she fulfils all her duties towards her husband. If he asks her [for his conjugal rights] even when she is on the back of a camel, she should respond to him.’” 

• At the same time, the Muslim should not forget, when his desire is provoked, to bear in mind the intention of keeping chaste and of enjoying that which is good and permissible. Then doing that will be an act of righteousness on his part, as the Prophet (peace and blessings of Allah be upon him) said: “In the intimacy of any one of you there is reward.” They said, “O Messenger of Allah, if any one of us fulfils his desire will there be reward for him in that?” He said, “Do you not see that if he does it in a prohibited way, that will be a sin on him? So if he does it in a permissible way, he will be rewarded for that.” (Narrated by Muslim, 1006, from the Hadith of Abu Dharr). A man should also recite the Du`a that was narrated from the Prophet (peace and blessings of Allah be upon him) for this situation. The Prophet (peace and blessings of Allah be upon him) said: “When any one of you wants to have intercourse with his wife, let him say: ‘Bismillaah, Allahumma jannibna ash-Shaytana wa jannib ash-Shaytana ma razaqtana (In the name of Allah, O Allah, keep the devil away from us and from that with which You may bless us)’, then if it is decreed that they should have a child from that, the devil will never be able to harm him.” (Narrated by Al-Bukhari, 6388; Muslim, 1434, from the Hadith of `Abdallah ibn `Abbas)

 May Allah grant you strength and bless you.