Does the newer 7961 phones work with the older 7914 side mods? I'd like to know before I purchase.
Yes, you are good to go with this combination:) I just set a couple up the other day. Here is some related info;
The Cisco Unified IP Phone Expansion Module 7914 extends the capabilities of the Cisco Unified IP Phones 7960G, 7961G, 7970G and 7971G-GE with additional buttons and an LCD display. With this expansion module, you add 14 buttons to the existing six buttons of the Cisco Unified IP Phones 7960 and 7961G and the existing eight buttons of the Cisco Unified IP Phones 7970G and 7971G-GE, increasing the total number of buttons when you add one or two Cisco Unified Expansion Modules 7914. You can use up to two Cisco Unified IP Phone Expansion Modules 7914 with a Cisco Unified IP Phones 7960G, 7961G, 7970G or 7971G-GE
From this good doc;
Hope this helps!