Assuming you have the same file in each of the addons. Simply changing the frame name on line 8 as well as setting f to be local not global ( that would mess things up there ) and the frame_x and frame_y values on lines 6 and 7 might be all you need to do. Assuming the rest of the code does what the addon was designed to do.
So..
Addon 1
Lua Code:
local frame_x = 0
local frame_y = -200
local f = CreateFrame("Button", "ZAMTimer1", UIParent, "BackdropTemplate")
Addon 2
Lua Code:
local frame_x = 0
local frame_y = -250
local f = CreateFrame("Button", "ZAMTimer2", UIParent, "BackdropTemplate")
Although I see you have the frame dragging code set up to re-arrange as needed. So, the above should work well enough to make both frames separate and accessible and not overidden by the other one.
I think having the f - CreateFrame line not be local was the main issue.