All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
At first, we state that it is completely forbidden for a woman to prevent her husband from having sex with her unless there is a confirmed harm. But a wife's decision to stop pregnancy for a certain period of time does not justify preventing her husband from having sex with her as he likes and as it is approved by the Sharee'ah. If she abides by such a prevention, then she becomes a disobedient wife.
Here, we say that Allah, The Great and Almighty, has stated the treatment of such recalcitrant (disobedient) wife, as He Says (what means): {But those [wives] from whom you fear arrogance - [first] advise them; [then if they persist], forsake them in bed; and [finally], strike them. But if they obey you [once more], seek no means against them. Indeed, Allah is ever Exalted and Grand.} [Quran 4:34]
So, the inquirer knows that to cease having sex with his wife is a form of punishment. But such a form of punishment should be the second step after admonition and reminding her of her duties, and this should not exceed the proper limits; i.e., the period of four months.
A husband's third step to deal with his disobedient wife is to beat her, but in a harmless and mild way that breaks no bone nor cuts the body.
As for birth control; i.e., to delay your wife's pregnancy for some time, we say that there is no objection as long as (1) there is an agreement between you and your wife, and (2) it is done according to the rules stated in the first decision of the 5th session of the Fiqh Assembly, held in Kuwait about birth control.
The above-mentioned decision states the following two points:
1 - It is forbidden both for men and women to eradicate (excise by surgery) the ability of procreation; i.e., to make one sterile unless there is dire need that also should be evaluated and controlled by the Sharee'ah standards.
2 - It is lawful to have temporary birth control solely to give longer periods between pregnancies or to prevent it for a specified period of time if there is need that is approved by the Sharee'ah. This state can be judged by mutual consultation between a husband and his wife, depending on legal means and avoiding any harm to existing pregnancy.
Therefore, if you agree to your wife's request provided that it should be for a specified period and it should not cause bodily harm or violation of some rulings of the Sharee'ah due to the use of contraceptives for birth control, then there is no blame on you to do so, just to keep your good marital relation and to satisfy her lawful desire.
For more benefit on permanent birth control, please refer to Fataawa 119261, 83837, 134895, 87304, 89857 and 84086.
Allah knows best.