She had an operation to prevent pregnancy permanently, then she and her husband regretted it

Undoubtedly you made a great mistake by doing that. Perhaps
you are aware that Islam encourages us to have children and that the Prophet
(peace and blessings of Allaah be upon him) encouraged men to marry
women who are loving and fertile, and that he (peace and blessings of
Allaah be upon him) will be proud of our great numbers before the other
nations on the Day of Resurrection. See question no.
11885. 

Whatever the case, you have to consult experts in the field
to find out whether it is possible for you to reverse the operation and put
things back to the way they were. If that is not possible, then you have to
repent and seek forgiveness, and do not despair of the mercy of Allaah. 

You should note that the son of Adam commits sin, and the
best of those who commit sin are those who repent. 

It was narrated from Anas that the Prophet (peace and
blessings of Allaah be upon him) said: “Every son of Adam commits sin, and
the best of those who commit sin are those who repent.” Narrated by
al-Tirmidhi, 2499; Ibn Maajah, 4251; classed as saheeh by al-Albaani in
Saheeh al-Jaami’, 4515. 

Indeed, Allaah rejoices over the repentance of His slave and
He is the One Who enables him to do that, although He has no need of His
creation. 

It was narrated that
al-Nu’maan ibn Basheer said: The Prophet (peace and blessings of Allaah
be upon him) said: “Indeed, Allaah rejoices over the repentance of His slave
more than a man who loads his provision of food and drink on a camel, then
he travels until he is in a wilderness, then the time  for the siesta comes,
so he dismounts and takes a nap under a tree, but he falls into a deep sleep
and his camel gets away, then he wakes up and he climbs one hill but he sees
nothing, then he climbs another hill but he sees nothing, then he climbs a
third hill but he sees nothing. Then he goes back to the place where he took
his nap and whilst he is sitting there, his camel comes walking towards him
until it puts its reins in his hand. But   indeed Allaah rejoices more
greatly than this man when he finds his camel.” Narrated by Muslim, 2745. 

And you should always be keen to recite “Sayyid
al-Istighfaar” (the best of prayers for forgiveness), which was narrated
by Shaddaad ibn Aws (may Allaah be pleased with him) from the Prophet
(peace and blessings of Allaah be upon him): 

“The best of prayers for forgiveness is: Allaahumma anta
rabbiy laa ilaaha illa anta, khalaqtani wa ana ‘abduka wa ana ‘ala ‘ahdika
wa wa’dika ma astata’tu. A’oodhu bika min sharri ma sana’tu, aboo’u laka bi
ni’matika ‘alayya wa aboo’u laka bi dhanbi, faghfir li fa innahu laa yaghfir
al-dhunooba illa anta (O Allaah, You are my Lord, there is no god but
You. You have created me and I am Your slave and I am keeping my promise and
covenant to You as much as I can. I seek refuge with You from the evil of
what I do. I acknowledge Your blessing and I acknowledge my sin, so forgive
me, for there is none who can forgive sin except You).” He said: “Whoever
says this during the day, believing in it firmly, and dies on that day
before evening comes, he will be one of the people of Paradise, and whoever
says it at night, believing firmly in it, and dies before morning comes, he
will be one of the people of Paradise.” Narrated by al-Bukhaari, 5947. 

You should choose the best of times to pray for forgiveness,
which is the last third of the night. Allaah says, praising His believing
slaves (interpretation of the meaning): 

“and those who pray and beg Allaah’s Pardon in the last
hours of the night”

[Aal ‘Imraan 3:17] 

It was narrated from Abu Hurayrah that the Messenger of
Allaah (S) said: “Our Lord descends to the lowest heaven each night during
the last third of the night, and He says: ‘Who will call upon Me, that I may
answer him, who will ask of Me, that I may give him, who will ask My
forgiveness, that I may forgive him?’” 

Narrated by al-Bukhaari, 1094; Muslim, 758. 

Since the husband is keen to have more children, he may also
take a second wife, from whom Allaah may bless him with good and righteous
offspring.  

And Allaah knows best.