Praise be to Allah

Firstly: 

Islam prohibits keeping dogs in general terms, but grants a concession allowing it in cases where people need that, such as guarding farms and hunting. 

It was narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever acquires a dog that is not a dog for herding livestock, hunting or watching the fields, one qiraat will be deducted from his reward every day.”. Narrated by al-Bukhaari (2322) and Muslim (1575). 

It was narrated that Ibn ‘Abbaas (may Allah be pleased with him) said: I heard Abu Talhah say: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “The angels do not enter a house in which there is a dog or an image.” Narrated by al-Bukhaari (3225) and Muslim (2106). 

Other matters for which there is an extreme need may also be included in these exceptions, such as guarding houses. 

An-Nawawi (may Allah have mercy on him) said: 

Our companions and others are unanimously agreed that it is prohibited to keep a dog for no purpose, such as keeping a dog because one likes the way it looks, or to show it off and feel proud of it. This is haraam, and there is no difference of scholarly opinion concerning that. 

With regard to the needs that make it permissible to keep dogs, there is this hadith which grants a concession allowing it for one of three purposes, namely guarding the fields, guarding livestock and hunting. These things are permissible, with no difference of scholarly opinion.

Our companions differed with regard to keeping dogs for the purpose of guarding houses and routes, and with regard to keeping puppies for the purpose of training them. 

Some of them regarded it as haraam, because the concession was only narrated concerning the three things mentioned above. 

Some of them regarded it as permissible, which is the more correct view, because those things come under the same heading. 

End quote from Sharh Saheeh Muslim (3/186). 

Secondly: 

Islam does not allow selling dogs, and regards their price as haraam. 

It was narrated from Abu Mas‘ood al-Ansaari (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) forbade the price of a dog, the payment of a prostitute and the fee of a fortuneteller. Narrated by al-Bukhaari (2237) and Muslim (1567). 

An-Nawawi (may Allah have mercy on him) said: 

With regard to the prohibition on the price of a dog, and the fact that it is among the worst kinds of earnings and among the most evil, this indicates that it is prohibited to sell dogs, and that the transaction is not valid and the price is not permissible, and they have no value for which the one who destroys them may be held liable, regardless of whether the dog was trained or not, and regardless of whether it was one that it is permissible to keep or not. This is the view of the majority of scholars, including Abu Hurayrah, al-Hasan al-Basri, Rabee‘ah, al-Awzaa‘i, al-Hakam, Hammaad, ash-Shaafa‘i, Ahmad, Dawood, Ibn al-Mundhir, and others. 

End quote from Sharh Saheeh Muslim (10/232-233. 

Ibn al-Qayyim (may Allah have mercy on him) said: 

Ibn ‘Umar said: The Messenger of Allah (blessings and peace of Allah be upon him) issued instructions that all dogs be killed except hunting dogs or dogs for herding sheep and livestock. ‘Abdullah ibn Mughaffal said: The Messenger of Allah (blessings and peace of Allah be upon him) instructed us to kill all dogs, then he said: “What is the matter with them and dogs?” (meaning that they should stop killing dogs) Then he issued a concession regarding hunting dogs and sheep dogs.

Both hadiths are narrated in as-Saheeh. 

This indicates that the concession allowing hunting dogs and sheep dogs was granted after the order to kill all dogs, because the dogs that the Messenger of Allah (blessings and peace of Allah be upon him) allowed people to keep are those the price of which he prohibited and stated that it is evil earnings, not dogs that he issued instructions to kill. The dogs that were ordered to be killed did not survive such that the community would need an explanation of the ruling on their price, and it was not customary to buy and sell them, unlike the dogs for which permission is given to keep them. The need for an explanation of the ruling on their price is greater than the need for an explanation on those that were not customarily bought and sold, and in fact they had been instructed to kill them. 

One of the things that clarifies this is the fact that the Prophet (blessings and peace of Allah be upon him) mentioned four things on which money is usually spent, because people are keen to acquire them, namely the money that is taken by prostitutes, fortunetellers, cuppers and sellers of dogs. So how could this be interpreted as referring to dogs that are not ordinarily bought and sold, and as excluding dogs that are ordinarily bought and sold. That is clearly not possible. 

End quote from Zaad al-Ma‘aad (5/701-702) 

It says in Fataawa al-Lajnah ad-Daa’imah li’l-Buhooth al-‘Ilmiyyah wa’l-Ifta’ (13/36-37): 

It is not permissible to sell dogs, and their price is not halaal, whether they are guard dogs, hunting dogs or other kinds, because of the report narrated by Abu Mas‘ood ‘Uqbah ibn ‘Amr (may Allah be pleased with him), who said: The Messenger of Allah (blessings and peace of Allah be upon him) forbade the price of a dog, the fee of a prostitute and the fee of a fortuneteller. Saheeh – agreed upon. 

And Allah is the source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and companions. End quote. 

Shaykh ‘Abdullah ibn Qa ‘ood, Shaykh ‘Abdullah ibn Ghadyaan, Shaykh ‘Abd ar-Razzaaq ‘Afeefi, Shaykh ‘Abd al-‘Azeez ibn ‘Abdullah ibn Baaz. 

Based on that, it is not permissible for you to work in selling dogs, even if they are trained. 

Similarly, it is not permissible for you to keep them or rent them out, because renting is a kind of selling, so it is included in the hadiths which forbid selling dogs and describe their price as haraam. 

Ibn Qudaamah (may Allah have mercy on him) said: 

That which it is not permissible to rent out falls into several categories:

… The third category is that which it is prohibited to sell, except a free man, a waqf, or an umm walad (a female slave who has borne a child to her master); it is permissible to rent them out (to do work), even though it is prohibited to sell them. Anything other than that it is not permissible to rent out. 

So it is not permissible to rent out dogs or pigs under any circumstances. End quote from al-Mughni (8/133) 

Al-Mardaawi said in al-Insaaf (9/401): 

It is not permissible to rent out dogs under any circumstances, according to the correct scholarly view, and this is the view of our companions. End quote. 

Zakariyya al-Ansaari ash-Shaafa‘i (d. 926) said in al-Gharar al-Bahiyyah fi Sharh al-Bahjah al-Wardiyyah (3/315): 

It is invalid to rent out a dog to guard the fields, herd livestock, guard a route or for hunting, because the benefit thereof carries no value in sharee‘ah. End quote. 

And Allah knows best.