Your PC can invent a new technique on his own
Taken from wikipedia's entry on the Southern Praying Mantis kung fu style:
Praying Mantis
The association of the term "Praying Mantis" with the style is also controversial. Each branch of the style offers a different explanation.
The traditions of the Chow Gar and Kwong Sai Jook Lum branches each maintain that their respective founders Chow Ah-Nam and Som Dot created their styles after witnessing a praying mantis fight and defeat a bird. Such inspiration is a recurring motif in the Chinese martial arts and can be found in the legends of Northern Praying Mantis, both White Crane styles, T'ai chi ch'uan, and Wing Chun.
If your rogue is observant enough - he may become inspired by some natural phenomenon, gaining insights about efficient and effective motions useful for offense, defense and maneuvering.
He doesn't need to be an acetic philosopher (though he may grow to become one as he advances) - he just needs the conviction and self-discipline to push him to go through the physical training required to hone his technique.
If your group's play style allows placing more emphasis on narrative at the cost of poorer combat optimization, you can even select to make the transition of your PC's reliance on his new martial skills gradual - continue wearing armor, combine armed attacks with unarmed strikes (not necessarily in the same round, though), etc. But, eventually your PC will start feeling that his armor is limiting him, preventing him from escaping blows that using his technique he can now avoid - then he may consider giving up on wearing armor. Same goes for unarmed strikes - have him hold on to his dagger, but occasionally use a flurry of blows(1) using a fist and an elbow of his other, empty hand - and let him realize that his hands have become faster and more accurate and than any weapon he is used to. This can lead him to relinquish the use of melee weapons, to use an interchanging combination of weapon and unarmed strikes or perhaps even seek "better" weapons which are more compatible with his developing abilities.
Bottom line - just because the "metagame concept" says your PC can now do something, doesn't automatically means he is aware of that and trusts himself enough to give up his old ways completely and immediately.
Or, he can find written records of a technique
Taken from wikipedia's entry on the Northern Praying Mantis kung fu style:
Origins
There are many legends surrounding the creation of Northern Praying Mantis boxing. One legend attributes the creation of Mantis fist to the Song Dynasty when Abbot Fu Ju [...] supposedly invited Wang Lang and seventeen other masters to come and improve the martial arts of Shaolin.
The Abbot recorded all of the techniques in a manual called the Mishou ("Secret Hands")
[...]
This manual supposedly disappeared until the Qianlong reign era,
[...]
The manual records Wang Lang "absorbed and equalized all previous techniques" learned from the 17 other masters.
Aside from self mastering a technique, your rogue may find a documentation of a certain technique - this can come instead of having him invent it from scratch, or as a latter supplement giving him more inspiration and advanced abilities.
At either case, you can probably work the narrative details with your GM so they won't clash terribly with the campaign settings (assuming that having a monk in it doesn't do that in the first place).
(1) Or whatever equivalent term used in 5e for that...
Monks can be tanky, but it requires both high Wisdom and high Dexterity. With a 18 in each stat, you'll have an AC of 18. They are not the best tanks though, and generally shine at taking down many weaker enemies, rather than soaking up damage themselves (especially at earlier levels).
However, if the DM allows you to choose the goliath race from the Elemental Evil Player's Companion, you gain access to the Stone's Endurance trait, which will allow you to mitigate 1d12 damage per short rest.
In addition, if your DM allows you might want to ask about being able to use the Way of the Unmoving Mountain (a homebrew path), which will allow you to mitigate 1d6 damage as a reaction and by using ki points.
The Combat Reflexes feat was removed and is not part of 5e currently.
If your group really needs a tank, you are better off with a Barbarian or Paladin, and multi-classing to Monk when you feel it acceptable.
Best Answer
If you're allowed to use variant human, take the Magic Initiate feat, choose Druid as the class, and take Shillelagh as one of your cantrip selections. Shillelagh lets you use your Wisdom Modifier for attack rolls with a Quarterstaff or similar weapon. (Note though this won't apply to your unarmed strikes unless your DM rules it that way.)
This also nets you one other Druid cantrip, and a first level Druid spell once per day. For Friar Tuck, may I suggest Goodberry to make Goodberry Wine.
Another thing to note, is that a Monk, while able to use Dex for Unarmed Strikes and Quarterstaff strikes, does not have to and may instead use Strength for both attack and damage rolls.
Keep in mind, this will leave you with lower AC than usual if you don't wear armour, and if you do wear armour you will lose out on your Martial Arts and Unarmoured Defense features.