There were suitable suitors if one applies most peoples' criteria. The problem is that Emily's father thinks no one is good enough for his daughter. He strongly discourages anyone from even trying to get close to his daughter, meaning he is the only one who ever gets to know Emily in any sense. He is extremely controlling, but we have to remember that he is a product of the Old South. He does not adapt to any societal changes.
As a result, Emily, too, is a product of the Old South, since her father is essentially her only "teacher." She, therefore, strikes townsfolk as snobby and crazy because she is so different. She, too, refuses to adapt to society's changes.
When she meets Homer Barron, who we are told is not interested in marriage at all, her twisted mind creates an ideal mate. Homer only wants good times and fun, not a serious commitment. When Emily realizes this, as she attempts to prepare them for the wedding she wants, she does the only thing she thinks she can do. Rather than lose the only man who ever got close to her or loved her (except her father, of course), she murders him. Keeping his corpse in the bridal bed is her way of maintaining her ideal.
In essence, the only man who is truly suitable for Emily is a dead man.
The suitors were considered "unsuitable" by Emily's father only. I'm sure several of them were suitable, but Emily's father felt no one was good enough for his "little girl". He kept her isolated from everyone and put her on a pedestal. Some critics have suggested the father might have been sexually abusive to Emily, but this is only conjecture. In the very least, Emily's father made her so dependent on him that when he died, she wouldn't let the town take his body for three days. This is mental abuse since Emily really didn't function well within society after her father's death.
Miss Emily is deprived of a husband by her father. He is domineering and controlling and finds all suitors unsuitable. He rejects all gentleman callers as not good enough for his daughter.
"Certainly Emily learns her genteel ways from him. It is his influence that deprives her of a husband when she is young;"
The narrator tells us in the story:
"We remembered all the young men her father had driven away," (Faulkner)
Then, of course, when Miss Emily meets Homer Barron and everyone in town thinks that they will marry, she discovers that he prefers the company of men.
"When she had first begun to be seen with Homer Barron, we had said, "She will marry him." Then we said, "She will persuade him yet," because Homer himself had remarked--he liked men, and it was known that he drank with the younger men in the Elks' Club--that he was not a marrying man."