A word for a man who offers his services to have sex with a woman unable to conceive

Solution 1:

I have heard of such ads... we call them inseminators.

Solution 2:

He's not a surrogate father, but he could be considered a sexual surrogate, or more specifically a male sexual surrogate.

Another common name would be sperm donor, although his suggested method of donation inclines one to question his professionalism.

Solution 3:

A stud farm is utilized in the domain of animal husbandry for the purpose of breeding animals. It says,

Male animals made available for breeding to outside female animals are said to be "standing at stud", or at "stud service"...

Although stud has certain less-desirable connotations, it might be applied in this circumstance.