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Excerpt from A Dictionary of Intermediate Japanese Grammar:

Consider the difference in the sentences below:

> [a] 昼間遊ぶ代わりに夜遊ぶつもりだ。  
> I intend to play at night instead of having fun in the daytime.
>
> [b] 昼間遊んだ代わりに夜勉強した。  
>  I played in the daytime, so (to make up for it) I studied at night.
>
> [c] 昼間遊んだ代わりに勉強するつもりだ。  
>  I played in the daytime, so (to make up for it) I intend to study at night.
>
> [d] 昼間遊ぶ代わりに夜遊んだ。  
>  I played at night instead of playing in the daytime.

* * *

I shall generalise the sentences to the form [X]代わりに[Y].

For [a] and [d], X and Y are regarding the same activity (遊ぶ). So when used
with 代わりに, Y occurs while the action is not performed at X.

For [b], X and Y are separate activities (遊ぶ and 勉強 respectively). When used
with 代わりに, both X and Y have the activity carried out.

I think where I'm having trouble understanding is becoming evident. There
seems to be a missing construction where X and Y are separate activities, and
only Y is carried out.

I'm trying to convey "I studied at night instead of playing in the daytime"
(The action of playing is not carried out).

I know that there are ~ないで and ~ずに that does approximately the same thing, but
they create sentences that are "Without X, do Y" which does not have the
nuance that "instead" creates, which is "Do Y in place of X"

**(Question)** Can 代わりに do what I'm trying to do? If yes, how? Or must I use a
different word altogether?

* * *

References:  
1: A Dictionary of Intermediate Japanese Grammar, Seiichi Makino and Michio
Tsutsui (ISBN4-7890-0775-8)
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question
grammar word-choice
"Instead" using 代わりに
I believe this works: "I studied at night instead of playing in the daytime"
昼遊びをしなかった代わりに夜に勉強しました。

Although it sounds a little strange to me because "studying at night" seems
like it doesn't make a good replacement for "playing in the daytime" mostly
because they take up different time slots.

Here's a more fitting example from alc. Note the contrasting connection
between the two activities which makes 代わりに fit well.

見学料をとられなかった代わりに、写真1～2枚なら買ってあげよう、と私は思った。 In place of the entrance fee, I
figured I would buy one or two photographs to help them out.
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There are two different usages for `代わりに`, and the problem comes from mixing
them up. You cannot distinguish them syntactically. Just look at the meaning
to distinguish them.

  * 'X instead of Y' (X is done; Y is not done)

> 昼間遊ぶ代わりに夜遊ぶ。  
>  'play during the night instead of playing during the day'

  * 'X in exchange for Y' (X and Y are done)

> 昼間遊ぶ代わりに夜勉強する。  
>  'study during the night to make up for playing during the day'

Once you notice these usages, it might not look unnatural that there is no
construction meaning that X is not done and Y is done.
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If you want to say “I studied at night in place of playing in the daytime”
using 代わりに, then you can use 昼遊ばなかった代わりに夜勉強した. However, I cannot imagine the
context where studying at night can replace playing in the daytime, and
therefore these sentences (both the English one and the Japanese one) look
unnatural to me. If there is such a context, then both sentences will become
natural in that context.
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