I think including "manga cafe" as a gloss is a good move. 
Still not sure coffeeshop is a more apt description than 
Internet café but I'll roll with it.

and まんが喫茶 (daijr) is the winner of n-grams

@@ -5 +5 @@
-<keb>マンガ喫茶</keb>
+<keb>まんが喫茶</keb>
@@ -9,0 +10,8 @@
+<k_ele>
+<keb>マンガ喫茶</keb>
+</k_ele>
+<r_ele>
+<reb>まんがきっさ</reb>
+<re_restr>まんが喫茶</re_restr>
+<re_restr>漫画喫茶</re_restr>
+</r_ele>
@@ -13,4 +20,0 @@
-</r_ele>
-<r_ele>
-<reb>まんがきっさ</reb>
-<re_restr>漫画喫茶</re_restr>

also 漫画 is a better x-ref for those who don't know what it means.

@@ -20 +20 @@
-<xref type="see" seq="2150290">漫喫</xref>
+<xref type="see" seq="1526920">漫画</xref>

https://en.wikipedia.org/wiki/Manga_cafe
-----
wikipedia separates 漫画喫茶 and インターネットカフェ for a reason
https://ja.wikipedia.org/wiki/インターネットカフェ
vs.
https://ja.wikipedia.org/wiki/漫画喫茶

-but an 'internet cafe' by definition has internet, whereas a マンガ喫茶 does not.  by definition, a マンガ喫茶 has manga...  internet is very common but optional.
-a bigger problem is the 'can read manga'.  that's what wikipedia says, but you 'can read manga' at any cafe if you BYOM.  the key is that they have their own library, as gg5 suggests.
-also, not really an abbr.  喫茶 is the abbr, which i have indicated in its own entry

@@ -21,2 +21,2 @@
-<misc>&abbr;</misc>
-<gloss>coffee shop or cafe where one can read manga, often has Internet facilities</gloss>
+<gloss>manga cafe</gloss>
+<gloss g_type="expl">coffee shop with a manga library (usu. has Internet facilities and charges by the hour)</gloss>

the point I was making with the wiki quote is that the word is most often used interchangably with ネットカフェ, but they do need to 
stock manga to make it a mangakissa. That seems to make them into "Internet cafés stocked with manga" rather than "coffee shops 
with manga and Internet".

These quotes aren't cherrypicked, I just googled "ネットカフェ マンガ喫茶 違い" and this is what came up:

http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1219857217
"[Q:] 漫画喫茶とネットカフェの違いを教えて下さい。
[BA:] ... 漫画があるかないかの違いなんでしょうかね？
[another answer:] まず「現在の違い」で言いますと「同じ」です。
[another answer:] 本来は、漫画の読める場所・インターネットに接続できる場所と区別されていたのだと思いますが、今はほとんどの店舗で漫画・ネット共に置いてありますね。 ... 
この二つが段々と一つになってしまったんでしょうね。
または「ネットカフェ」自体が、漫画やゲームの出来る複合施設を意味するのかもしれません。"
http://netcafe.sakura.ne.jp/work/mankitsu.html
"ネットカフェ、ネカフェ、漫画喫茶、マンキツ、複合カフェなど、様々な名称で呼ばれていますが、どれも同じです。"
http://plaza.rakuten.co.jp/shion0851zatta/diary/200704120000/
"ネットカフェと漫画喫茶。
この２つの差というか違いは、以前はPC（ネット）と漫画の有無でしたが、今ではほとんどの店で兼備しているのでほとんど違いはありません。

The very first hit for mangakissa ( http://www.cafeman.jp/ ) has this quote: 全国のインターネットカフェ/まんが喫茶を掲載！ and in the flash 
navigation below, it says "ネットカフェナビ"
http://www.cafeman.jp/

There probably used to be a clear distinction between ネットカフェ and マンガ喫茶, but it seems almost non-existent by now. Modern マンガ喫
茶 have way much more in common with (Japanese) internet cafés than coffeeshops.