Your question is based in a few false suppositions- that the northern states "allowed" the southern states to be apart of the union, that slavery was unpopular at the time , that the northern states had abolished slavery and that the Framers and the Founding generation foresaw the coming troubles the nation would face as a result of the debate over slavery.

Lets tackle the last supposition first. The Civil War occurred 73 years after the Constitution was written. Do you know what is going to happen in 2093? (If you do let me know I have questions) No one in 1787 knew what was going to happen in the country over the coming years let alone the next day. So yes of course if we know what is going to happen in the future we can make attempts to prevent it but since we don't and neither did the Founding generation the point is rendered moot. Discussing the Civil War is the sort of thing that my favorite superhero would bring up- https://www.youtube.com/watch?v=gdbjw27QPJQ

The United States wasn't some club that the northern states had admission rights to. It wasn't that some states weren't allowed to be in the club and others were. All of the states were a part of the United States. This collective mentality can be traced back to the First and Second Continental Congress. While the colonies, and later states, all had their differences, (as they do today) from the onset their collective union was assumed. To quote the Declaration-

"...in the Name, and by Authority of the good People of these Colonies, solemnly publish and declare, That these United Colonies are, and of Right ought to be Free and Independent States..."

The states, generally, acted in concert with each other, even though they argued and disagreed constantly about everything (like today). When the Articles of Confederation were passed onto the states for ratification it had to be unanimous. (It was quickly ratified with Maryland as the lone holdout until Virginia relinquished some western claims) The Articles full name is, The Articles of Confederation and Perpetual Union- the union of the 13 states was assumed. So it wasn't that any of the 13 states had to be allowed into the union they were already in it they just had to agree what that union looked like.

Now for the bulk of it-slavery

Although the Founding Generation believed slavery to be dying (once again we can see how they couldn't predict the future) and some were outright opposed to it, many northern states maintained slavery well into the 19th Century. In fact only Rhode Island, Pennsylvania, Connecticut, and Massachusetts had abolished slavery when the Constitution was written.

New York would abolish slavery in 1799 but it only freed the children of slaves born after 1799 and even then they were indentured until they were young adults. In 1817 NY freed slaves born before 1799 but not until 1827.

New Hampshire only abolished slavery in 1857-YES you read that right 1857- but slavery was already dying in NH. In fact the 1800 census only counted 8 slaves and after 1840 there were no more recorded slaves in the state. So while NH didn't outright abolish it, it was an already unpopular system (whether morally or economically).

New Jersey was the last northern state to abolish slavery in 1804 with the Gradual Abolition Act. Children of slaves born after July 4 1804 were considered indentured servants- girls until 21 boys until 25. Even then the act didn't guarantee that someone born after 1804 was freed, often NJ slave owners would sell to southern slave owners. It wasn't until 1846 that slavery was abolished but slaves born before July 4 1804 were considered indentured servants for life. It wasn't until the 13th Amendment that slavery was finally gone from NJ.

Slavery at the Convention

When the Constitutional Convention was convened the states came to the Convention to create a Constitution for the country as they knew it existed. Since slavery was part of the Union, it had to be dealt with, just like taxes, relationship between the states and the national government or foreign relations. The new nation was frail and needed agreement and acceptance by all the states. This meant that because each state had different interests, compromises needed to be made in order to create a document that best represented the Union as a whole. We need to acknowledge that the compromises over and the acknowledgment of, slavery in the constitution is not necessarily a failure of the Framers or the Founding Generation.

But the Framers also came to the convention with the knowledge that they had to create a document to stand the test of time. So they acknowledged slavery while also limiting it. They foresaw that slavery’s importance would eventually diminish (even though they were wrong about that), but they needed a Constitution that would guide them through both the present and the future of the Union. The Constitution contains 3 clauses that deal with slavery- the 3/5's compromise, the slave trade abolishment, and the fugitive slave clause. All of these point to the fact that slavery was neither widely accepted nor expected to continue. (We can see an example of this with the prohibition of slavery in the Northwest Territories which was passed under the Articles of Confederation) All three clauses referred to slaves as "Persons" and not property. Also, the fact that the word "slave" was never written in the Constitution demonstrated that slavery was not accepted by all the Framers.

A close examination of the Constitution and the beliefs of the Framers indicates that the Constitution was a document that incorporated compromise. The Founding Generation and the Framers realized slavery was not an indefinite institution, but that it would eventually die out. They therefore created a document that represented the Union as it stood in 1787. Some provisions had to be made for slavery while also leaving the Constitution open to debate and change if and when slavery would be abolished. The most important point to remember is that the Constitution was established to uphold the Union and the rights and liberties of the people.