You will be required to make some unix calculations, but they will be simple ones.

See the code below:

{% assign today = 'now' | date: '%s' %}
{% assign single_day = 86400 %}
{% assign today_number = 'now' | date: '%u' | plus: 0 %}

{% if  today_number < 2 %} 

    Delivery by {{ today | plus: single_day | date: '%Y/%m/%d' }}

{% else %}

    {% assign days_until_next = 9 | minus: today_number  %}
    {% assign days_unix = days_until_next | times: single_day  %}
    Delivery by {{ today | plus: days_unix  | date: '%Y/%m/%d' }}

{% endif %}

I will try to break it down.

Assigning reusable data
{% assign today = 'now' | date: '%s' %} - with this we are getting the current unix timestamp for the server date

{% assign single_day = 86400 %} - this is the number that defines a single day in unix timestamp

{% assign today_number = 'now' | date: '%u' | plus: 0 %} - this returns the current day as a number (1...7). The plus: 0 is to convert it to a number instead of a string.

Condition
{% if  today_number < 2 %} - we are checking if today_number is smaller than 2 ( where 2 is Tuesday ), it can be written in this case like so as well {% if  today_number == 1 %}, but you get the logic

Output
If the above condition is true we do this:

{{ today | plus: single_day | date: '%Y/%m/%d' }} - this sums the timestamp today and the single_day timestamp, giving us the date tomorrow

If the if statement return false we go in the {% else %} statement where we set a few variables.

{% assign days_until_next = 9 | minus: today_number  %} - since we are counting from the 2nd day I'm using the number 9 as a base and substract the current today_number so for example if today is Tuesday, we have 2 and 9-2=7, so this means the next Tuesday is 7 days from now.

{% assign days_unix = days_until_next | times: single_day  %} - this just calculates the single day unix number times the days until the next Tuesday. So if we continue the above Tuesday example you get 86400*7=604800

{{ today | plus: days_unix  | date: '%Y/%m/%d' }} - finally we sum the today unix number with the unix number for the days until the next Tuesday and we convert it to a readable date.