A cursor will be fastest, but here is a SELECT query that will do it. Note that for "up to N" days apart instead of 2 you'll have to replace the table Two with a table of integers from 0 to N-1 (and the efficiency will get worse).
I'll admit it's not entirely clear what you want, but I'm guess you want the ranges of rows that contain at least two rows in all and within which the successive rows are at most 2 days apart. If dates increase along with IDs, this should work.
with Two as (
select 0 as offset union all select 1
), r2(ID, Date_Created_o, dr) as (
select
ID, Date_Created+offset,
Date_Created + offset - dense_rank() over (
order by Date_Created+offset
) from r cross join Two
)
select
min(ID) as start, max(ID) as finish
from r2
group by dr
having min(ID) < max(ID)
order by dr;