Sony Movie Channel will be featuring several Godzilla films during the month of September, most are the films that Sony has released on Blu-ray but also they will be showing Mothra '61 as well. Below are the listings from there site.

MOTHRA (1961)

Monday, Sept 1 11.20 am E | 8.20 am P
Friday, Sept 5 6.40 am E | 3.40 am P
Saturday, Sept 13 3.25 pm E | 12.25 pm P
Monday, Sept 22 9.00 am E | 6.00 am P
Monday, Sept 22 9.00 am E | 6.00 am P

GODZILLA VS. MOTHRA (1992)

Monday, Sept 1 9.30 am E | 6.30 am P
Friday, Sept 5 8.15 am E | 5.15 am P
Monday, Sept 8 10.00 pm E | 7.00 pm P
Monday, Sept 8 1.30 am E | 10.30 pm P
Monday, Sept 22 10.35 am E | 7.35 am P

GODZILLA 2000 (1999)

Monday, Sept 1 1.00 pm E | 10.00 am P
Monday, Sept 8 11.45 pm E | 8.45 pm P
Monday, Sept 8 3.15 am E | 12.15 am P
Thursday, Sept 11 6.25 am E | 3.25 am P

GODZILLA VS. MEGAGUIRUS: THE G ANNIHILATION STRATEGY (2000)

Monday, Sept 1 2.40 pm E | 11.40 am P
Monday, Sept 15 10.00 pm E | 7.00 pm P
Monday, Sept 15 1.20 am E | 10.20 pm P
Sunday, Sept 21 7.10 am E | 4.10 am P

GODZILLA AGAINST MECHAGODZILLA (2002)

Monday, Sept 1 4.35 pm E | 1.35 pm P
Monday, Sept 15 11.50 pm E | 8.50 pm P
Monday, Sept 15 3.10 am E | 12.10 am P
Sunday, Sept 21 9.00 am E | 6.00 am P

GODZILLA: TOKYO S.O.S. (2003)

Monday, Sept 1 6.10 pm E | 3.10 pm P
Thursday, Sept 4 6.05 pm E | 3.05 pm P
Thursday, Sept 11 8.10 am E | 5.10 am P
Monday, Sept 22 10.00 pm E | 7.00 pm P
Monday, Sept 22 1.50 am E | 10.50 pm P
Saturday, Sept 27 7.55 am E | 4.55 am P

GODZILLA: FINAL WARS (2004)

Monday, Sept 1 7.45 pm E | 4.45 pm P
Thursday, Sept 4 7.45 pm E | 4.45 pm P
Saturday, Sept 13 1.10 pm E | 10.10 am P
Monday, Sept 22 11.40 pm E | 8.40 pm P
Monday, Sept 22 3.30 am E | 12.30 am P
Saturday, Sept 27 9.30 am E | 6.30 am P

This exhibit opens today and runs through the 17th check out the info below and the link for more info (translated from the Japanese site).

Holding period 2014/08/02 (Sat) - 2014/08/17 (Sun)
Holding time 10:00 to 18:00 (last admission 17:30)
Venue Exhibition Hall A  World Import Mart 4F  
Fee ■ Advance tickets
for adults (junior high school or more) 1,000 yen 
(3 years old - elementary school students) ¥ 500 children
■ Day Ticket
Adult (junior high school or more) 1,200 yen for 
children (3 years old - elementary school students) 700 yen
Organizer Large Godzilla special effects Exhibition Executive Committee
Phone number (Up to 17 days 10:00 ~ 18:00 ※ 8 May) 03-6369-8105
URL http://www.godzilla-tokusatsu.com/
The number of great power exhibition on the heels of the 60th anniversary of Godzilla birth ways. 
Highlight full to the latest movie from the Godzilla series in history! ■ (Sat) 10:00 - June 21, 2014 Advance release launch in each play guide Seven ticket, Lawson Ticket, Ticket Pia, of e +!