Concession fares, at least on InterCity services are NOT available available off peak on weekends, they are charged the peak fare.
Direct from the online ticketing section of the V/Line Website:
Off Peak Concession/Child tickets are not valid for travel on weekends, so Peak Concession/Child fares apply for the return journey.
MYKI - concession can get a off-peak fares on the weekend
V/Line paper ticket - concession cant get a off-peak fare on the weekend
MYki - page 43 of the ticket book
Fares for all journeys in 3 or more zones receive an off-peak discount, except where touch off occurs
within Zone 1 before 9am on a business day or touch on occurs within Zone 1 between 4pm and
6pm on a business day.
Customers must touch on and touch off to receive the applicable off-peak discount. The discount for
off-peak travel is 30 per cent (this is applied after any concession discount). Customers who do not
touch on and off correctly will be charged a default fare that is a peak fare.
For customers travelling off-peak, the equivalent peak fare contributes toward the Daily cap, even
though a reduced fare is paid. For example when a full fare customer travels three zones off-peak,
100 per cent of the standard fare will be counted towards the Daily cap even though only 70 per cent
of the standard fare has been paid.
V/Line paper ticket: page 102
Peak/Off-peak ticket conditions
Customers with Off-peak Single and Off-peak Daily tickets may not travel on weekday services
scheduled to arrive in Melbourne (Southern Cross, Flinders St, Richmond or North Melbourne)
before 9am, or services scheduled to depart Melbourne between 4pm and 6pm.
Concession Off-peak Single and Concession Off-peak Daily tickets are not valid for travel on
weekends. Concession customers may use Concession Single or Concession Day Return tickets
on weekends. Full fare Off-peak Single and Full Fare Off-peak Daily tickets are valid (without time
restrictions) on weekends.
I get my information from legal documents : Victoria Gazette - http://www.gazette.vic.gov.au/gazette_bin/search_gateway.cfm?bct=home
other note: There no such thing as Two hour fare under myki it called Single fare!