Firstly: 

For a Muslim to make his brother happy and joke with him based on what is true is permissible in principle. It was narrated that Abu Hurayrah (may Allah be pleased with him) said: They said: O Messenger of Allah, you joke with us. He said: “I do not say anything but what is true.”

Narrated by at-Tirmidhi; classed as saheeh by al-Albaani in Saheeh at-Tirmidhi. 

Secondly: 

If the jokes and humour that people pass around among themselves are based on what is true, and do not contain any material that is unIslamic, such as mocking the religion and those who follow it, or making fun of specific individuals and mocking them, or promoting immorality and indecency, then there is nothing to say that they are not allowed, on condition that this is not done so much that it distracts the Muslim from that which is more beneficial for him. But if the content includes any of the things mentioned above, it is not permissible to deal with it and transmit it. According to the hadeeth, the Prophet (blessings and peace of Allah be upon him) said: “Woe to the one who speaks and tells lies in order to make the people laugh; woe to him, woe to him.”

Narrated by at-Tirmidhi, 2315; Abu Dawood, 4990. classed as hasan by al-Albaani in Saheeh at-Tirmidhi. 

Allah, may He be glorified and exalted, said (interpretation of the meaning):

“O you who believe! Let not a group scoff at another group, it may be that the latter are better than the former; nor let (some) women scoff at other women, it may be that the latter are better than the former, nor defame one another, nor insult one another by nicknames. How bad is it, to insult ones brother after having Faith (i.e. to call your Muslim brother (a faithful believer) as: "O sinner", or "O wicked", etc.). And whosoever does not repent, then such are indeed Zalimoon (wrong-doers, etc.)”

[al-Hujuraat 49:11]. 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked the following question: 

What is the ruling on jokes according to our Islamic religion? Do they come under the heading of idle speech? Please note that they are not making fun of the religion itself. Please advise us, may Allah reward you. 

He replied: Praise be to Allah. 

There is nothing wrong with humorous speech and telling jokes if it speaks about things that are true, especially if one does not do it too much. The Prophet (blessings and peace of Allah be upon him) used to joke but he never said anything but that which was true. But if the joke involves lying, then it is not permissible because the Prophet (blessings and peace of Allah be upon him) said: “Woe to the one who speaks and tell lies to make people laugh; woe to him, woe to him.”

Narrated by Abu Dawood, at-Tirmidhi and an-Nasaa’i with a jayyid isnaad. And Allah is the source of strength. 

Majmoo‘ Fataawa wa Maqaalaat li’sh-Shaykh Ibn Baaz, 6/391 

Thirdly: 

Based on the above, if the jokes that will appear on this application conform with these guidelines, there is nothing wrong with making this application. But if there is anything that is contrary to these guidelines or you do not have the ability to check or moderate the jokes that appear on the application, or to publish what is permissible whilst preventing what is not permissible, then in that case we think that you should not do that, lest it involve helping people in sin, or it opens the door to corruption and foul speech. 

If it is possible to make an alternative to this humorous application, such as an educational application that includes useful information and attracts their attention, and it could include some lighthearted from classical books, without it being only for that type of material, then perhaps this would be better and further removed from anything objectionable. 

And Allah knows best.