The pulp can be kept in the fridge for up to three days if you're not using it immediately. It could also be stored in the freezer.
If a recipe calls for a relatively small amount of pulp (around 200 to 300 g / 8 to 10 oz), you can do this by hand: assume you'll produce a roughly equal weight of well bletted fruit. Peel back the papery skin and discard, then peel the fruit to remove the five stones hidden in the pulpy mass by pushing the flesh through a large wire sieve into a bowl.