How do I type  on a keyboard? I am using the Google Cantonese Input and Google Pinyin Input on my phone and cannot find a way to type .  Even when I switch to the handwriting method,  does not come up as an option and I get them separated as 門小 instead.

How would I type  with Pin Yin or Yale/Jyutping input?  For now, I'm just using 屌你 instead of 你.  Otherwise, I would have to copy and paste  and it gets annoying.
One could always argue that if you find it annoying to copy/paste , you're using it too much, and should clean up your vocabulary :-)
It all depends on the platform you're using. I'm on a Mac (laptop) and Android (phone/tablet). On my Mac, I have customized an old Jyutping IME by Dominic Yu, based on the LSHK table. I added  (and many other things) to the IME. You can get it here.
On my Android, I use MultiLing, which is good in most cases, but its fuzzy logic makes it very hard to input single-syllable words that are not common (at least in their idea of common). I usually resort, for such characters, to trying first pinyin, then Japanese, or, if everything fails, hand-writing.
EDIT
On MultiLing, typing diunei gives 屌你, which is the fastest way I found to type 屌 – if 你 isn't needed just erase it.