My concern is that if they were to split up, then the other one would not be able to afford the rent on their own.Do I write a lease were the primary breadwinner is the sole leasee or do I just go ahead and write a joint lease where they are both on the lease and hope that they stay together.The candidates appear to be very responsible, clean and drove a clean car.

While you may help screen people that shouldn't come see the place, you will certainly lose some people that are good candidates and perhaps would have liked the apartment. 

If they passed your initial screening criteria, they should be potentially good tenant candidates. 

@Stephanie Simmons and Bjorn, I am thinking of just cutting ties with her and hope to find a better candidate.

The tenant is responsible for the rent until the unit is filled with a qualified candidate. 

Here's why:Let's say I sign a tenant to a one-year lease, and 3 months in, their personal/professional situation changes, and they break their lease and move out after a 30-day notice (or maybe less).I am required, by law in most areas, to "mitigate my loss" by remarketing the unit, making it rent-ready, and starting up my lead generation machine to get applicants, funnel them into my screening system, identifying good candidates and ultimately leasing them up.

@Noah Willard Have you actually ran the candidates credit, criminal, income, and eviction background to verify what they are claiming?

I just send them a message," thanks for your interest, we went with another candidate.

After providing me with a selection of candidates and any recommendations he may have, I make the decision on which tenant to place.

You might consider having a candid conversation with the tenant along the lines of "Look, you're clearly not happy here.