You can create a zap to trigger weekly, but use this template if you only want the zap to run alternate weeks. It uses a stored value to remember whether each week is a send or not send week.
First, create a zap that triggers every week. Then you need to add a'Zapier Storage' step to get or set a value. The key will be 'send' and the value will alternate between 'yes' and 'no'.
In the next step, we'll use a 'Formatter->Utilities->Lookup Table' step to switch the value to the opposite.
And then, we'll update the stored value to the reflect the new value.
Next, we add a filter step that compares the initial value from step 2 (not the newly stored value) and only continues if it was 'yes'.
After that, we can add any steps needed for the rest of them zap. When the zap runs again the next week, the value compared at the filter step will read 'no', so the zap will stop.