Раз тег не ORM, то можете погонять на своих тестовых данных SQL.
Подставьте ваш $date вместо
timestamp '2019-06-27 11:15:00'/*
with channel_program as (
select 1 as channel_id, 1 as program_id, timestamp '2019-06-27 09:00:00' as start_time, timestamp '2019-06-27 10:00:00' as end_time union all
select 1 as channel_id, 2 as program_id, timestamp '2019-06-27 10:02:00' as start_time, timestamp '2019-06-27 11:00:00' as end_time union all
select 1 as channel_id, 3 as program_id, timestamp '2019-06-27 11:10:00' as start_time, timestamp '2019-06-27 11:30:00' as end_time union all
select 1 as channel_id, 4 as program_id, timestamp '2019-06-27 11:35:00' as start_time, timestamp '2019-06-27 12:00:00' as end_time union all
select 1 as channel_id, 4 as program_id, timestamp '2019-06-27 12:00:00' as start_time, timestamp '2019-06-27 12:30:00' as end_time
)
*/
select t.program_id
from (
select
program_id
,lag(start_time) over (order by start_time) lag_start_time
,lead(end_time) over (order by start_time) lead_end_time
from channel_program
) t
where timestamp '2019-06-27 11:15:00' between coalesce(t.lag_start_time, timestamp '1991-01-01 00:00:00')
and coalesce(t.lead_end_time, timestamp '2999-01-01 00:00:00')