
In my breed they tend to be a verbal agreement. Generally unless there is to be a puppy in lieu, or free return, or no puppy no fee then there is no need for a contract, as the fee is usually paid once the mating has been witnessed, or when the bitch is picked up, and you should receive a signed litter registration form confirming the mating.
In some cases the Stud dog owner may wait until the litter is born, and will ask for the fee to be sent with the litter registration form to be signed by them confirming mating, as without this form the litter can't be registered, but this sort of arangement is often among people that know and trust each other.
If a contract is really wanted, then it will need to include the amount of fee, when payable, and if a free return will be provided if the bitch misses. If it has been agreed that a puppy will be taken in lieu of fee then it must be specified what sex, whether pick or second pick etc. Who will choose and when, and what happens if there is no live pups reared.