You can use queues and explicitly defined queue, but in this case you can just make use of a call back with .slideUp().
Since animations can be chained to add them to the default queue, you can just chain .slideDown() right after the .slideUp().
$(sliderSelector).slideUp(function() {
// delete and add stuff
}).slideDown();
jsFiddle example
If you are using custom slide up and slide down functionality with no call back, then I don't know if you have automatic queueing functionality added into the chaining either, so you can just create a queue on the fly using .queue():
$(this).queue(function() {
// Stuff to do
// ...
// Dequeue
$(this).dequeue;
});
So your whole code would be:
$(this).queue(function() {
$(this).customUp();
$(this).dequeue();
}).queue(function() {
// Delete & add stuff
// ...
$(this).dequeue();
}).queue(function() {
$(this).customDown();
$(this).dequeue();
});
jsFiddle example