Here's one possible solution. Create a function that takes a date as an input and calculates the cumulative count for that date and then returns the count. Then in your original query, replace the count(some_field) with a call to the function, passing the function the row's date.
create or replace function calc_cumulative_count(input_date DATE)
return LONG
as
cumulative_count LONG;
select count(your_field_name)
into cumulative_count
from your_table
where some_date_field <= input_date;
return cumulative_count;
end calc_cumulative_count;
/
If your exisiting query is
select some_date_field
,count(your_field_name)
from your_table
group by some_date_field
;
this can be changed to
select distinct some_date_field
,calc_cumulative_count(some_date_field)
from your_table
;