My realtor has taken several days to draw up a contract for a house. Is that normal?

Unless there are particular state requirements that need to be addressed or some other difficulties, no, the paperwork is in a computer and the blanks are filled in. I have seen them done in 1-2 days, delivered and signed

Which contract

Are you listing the home with them ?

Or are you making an offer on a home ?

To be honest, unless there are some confusing terms, or the agent is waiting on the broker to approve ( many agents have to get the broker to approve ) a few hours to a day, I would be asking if I needed another agent, if they did not do my offers within a day.

But again, what type of contract,

Rental
Purchase
Listing
Contract for deed

Or even closing paper work, ( which a agent should not be doing anyway