The best way is the following:

1. # run

 xkbcomp $DISPLAY layout.xkb 

2. Open layout.xkb with an editor, use search to find the line that starts with "key <BKSP>" and change it from:

   key <BKSP> {         [       BackSpace,       BackSpace ] };

To:

   key <BKSP> {         [      Caps_Lock,       Caps_Lock  ] };

3. # run

 xkbcomp layout.xkb $DISPLAY 

4. Rename it to something like .Xkeymap (that will make it hidden) and put it in $HOME.

5. Next, place this line in your .xinitrc, so that you don't have to redo step number 3 every time you login:

test -f ~/.Xkeymap && xkbcomp ~/.Xkeymap $DISPLAY

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As for the dead keys not working, I have no idea. Do they work in the tty?

I don't mean to be rude, but don't go ahead of yourself by installing arch based distros like manjaro. Even guru users often stick to mainstream distros, just for ease of support.

Let's check if the dead keys are defined in the first place. In your .Xkeymap, search for: key <AC05>
It should look something like this:

 key <AC05> {
1212         type= "FOUR_LEVEL_SEMIALPHABETIC",
1213         symbols[Group1]= [               d,               D,  dead_diaeresis,      asciitilde ]
1214     };

They probably are, but check to be sure.

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Next check if they are sent to X by starting xev from a terminal and press Altgr+d. Do you see it output "dead_diaeresis"?

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Also, do dead keys work in other layouts, or is this only a colemak problem?

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In any case, if I were you and needed these characters so much, I would bind them on the 3rd layer (AltGr) directly. It should be pretty easy to do this in the .Xkeymap file.

Nice I'm also a manjaro user switching to colemak (cold turkey from dvorak).

I'd have to say that screwing around with manjaro is less likely to break or be broken then
most of the (actually all) of the popular distros.
especially the most popular one which will remain nameless (mostly because things that >>usually<<
blow up on updates don't deserve a name).

kidding...kinda..