Clearly conflict is one of the major ingredients in this excellent short story, which is normally used to teach irony in schools. The major source of external conflict that Della faces is against poverty:
Tomorrow would be Christmas Day and she had only $1.87 with which to buy Jim a present. She had been saving every penny she could for months, with this result... Only $1.87 to buy a present for Jim. Her Jim. Many a happy hour she had spent planning for something nice for him. Something fine and rare and sterling - something just a little bit near to being worthy of the honour of being owned by Jim.
Della thus faces a conflict of how she is going to buy the present she wants to buy for her husband, whom she loves so much.
The internal conflict that Della faces is when she wants to sell her hair to gain the money to be able to buy the present for Jim. Note how the text describes this internal battle:
So now Della's beautiful hair fell about her rippling and shining like a cascade of brown waters. It reached below her knee and made itself almost a garment for her. And then she did it up again nervously and quickly. Once she faltered for a minute and stood still while a tear of two splashed on the worn red carpet.
The tears of course are evidence of the cost of this conflict, as she chooses to sacrifice her one possession in which she took "mighty pride" for the sake of her husband, so that she can buy him the present that she wants for Christmas.