Firstly: 

It is proven that the Prophet (peace and blessings of Allaah be upon him) forbade making vows, and he said that they are a means of getting something out of the miser. This prohibition is confirmed in the case of one who believes that he may get what he wants because of the vow, or that Allaah may give him what he wants because of his vow. 

It says in al-Mawsoo’ah al-Fiqhiyyah (40/140), discussing the ruling on vows: 

Al-Qurtubi said: It seems to me that making a vow is haraam in the case of the one who thinks that the vow is a means to achieving some end or that Allaah will give him what he wants because of the vow, so making the vow – in this case – is haraam, and it is makrooh in the case of one who does not believe that. End quote. 

How often we receive messages from people who made vows to do acts of worship, then they were not able to do them. What the Muslim should do is to guard his tongue and not make vows. The one who wants to give charity, fast or offer a sacrifice should do that without making a vow, so that he will not be putting himself under pressure: if he wants to refrain from that he may do so and there will be no blame on him, instead of exposing himself to the risk of not fulfilling the vow, which is a serious matter. 

See also the answer to question no. 42178. 

Secondly: 

‘Aqeeqah is a confirmed Sunnah, which should not be omitted by the one who is able to do it. This has been discussed in the answer to question no. 12448. 

If a person makes a vow to offer an ‘aqeeqah on behalf of his son, then he must do that, because the Prophet (peace and blessings of Allaah be upon him) said: “Whoever vows to obey Allaah, let him obey Him.” Narrated by al-Bukhaari (6696). 

If he is unable to fulfil this vow, then one of two scenarios must apply: 

1-

either he stipulated a specific time for slaughtering the ‘aqeeqah, whether he spoke that out loud or intended it, such as one who intends to slaughter it in the first week or the first month after the birth. If that specific time has passed and he was unable to fulfil his vow, then he must offer expiation for breaking an oath (kafaarat yameen), because the Prophet (peace and blessings of Allaah be upon him) said: “The expiation for breaking a vow is kafaarat yameen.” Narrated by Muslim (1645). 

2-

or he did not stipulate a specific time for slaughtering the ‘aqeeqah, so the ‘aqeeqah remains as a debt which he owes, until he is able to fulfil his vow, because there is no specific time for the ‘aqeeqah which he has missed, rather it is valid to slaughter it at any time, even if it is years after the birth. 

And Allaah knows best.