When using Rolling (Contract) billing, where the billing date is based on the start date of the membership (ie, one week, one month from contract start date) you can change their billing cycle as follows

1 - Expand Contract > 3 dot menu > Modify Billing Cycle

2 - Set the day of week/day in month that you want them to be billed
The calculated next bill date will display the next available date based on the Billing Day you select.  

3 - Calculate the prorate due from their old billing date to their new billing date.
To do this, calculate their "per day rate" (ie, weekly rate divided by 7; monthly rate divided by 30) and multiply by the number of days you are pushing the next bill date out with this change.  

For example, if they are billed weekly and the current next bill date is 8/4/25 and I am moving that to 8/7, i need to charge 3 days worth of membership (to cover the 4th, 5th, and 6th that would be skipped by this new next bill date), that way on 8/7 they are billed as normal for the week.
 

4 - (optional) Associate invoice with contract.