The best thing to do is message an individual teacher, present your idea and see what response you get. There could not be a search function for method because that is not how professional learning is organized. Can't imagine hiring a public school teacher not because of their degree, or their work experience, or their references from past students but because they specialize in using flashcards well, for example. Knowledge of HUGE VARIETY of techniques are such a small part of what a trained teacher brings to the table.

TPR is just one relatively simple method / technique that any professionally trained teacher knows of / can use.

IMHO, a trained professional teacher will do an informal assessment (ongoing assessment, actually) and then devise a path that suits the level, goals, needs and preferences of the learner.  Ideally...

Do you go to a restaurant and tell the chef how to make the salad?  :) 

You tell the chef what you want but you leave the method up to her, yes?

I'm curious what it is about Total Physical Response with stories that interests you?  Are you looking for lessons for a Young Learner?  That would be my first question -- what is the AIM / GOAL for which you've settled on TPR as your method? 

Some considerations:

How should the teacher CONVEY the meaning of the story (first), since comprehension usually precedes any kind of response from a learner?  How long is the story?  Sometimes student choose materials that aren't amenable to a single lesson.  Will it presented as a text (and what percentage of the words are at each level -- will any (what precentage) need to be pre-taught?  How much tolerance does the individual learner have for presentation activities that generally teacher-centred, learner-passive?

OR Will it be presented as an audio?  Does the student want to focus on listening (gist listening for the idea or to hear specific words / answer a list of progressively more difficult questions) OR Is it about vocabulary (Do you want to hear explanations / meanings?  What persentage of the vocabulary is known to the learner and what percentage would be new?  Do you want to make example sentences?  Is the point for the learner to practice hearing and responding to known vocabulary (consolidation) or is about speaking and using the vocabulary?

etc etc

Hi,

I think italki lacks a search interface that goes beyond the basic. Nevertheless, I don't think it would be easy - if possible - to let us filter a search based upon methodology choices. I believe that it's something difficult to find out even by just reading their profile.

What I've done so far is reading lots of profiles, checking their education and work experience, something you've probably been doing.

I do believe each teacher has his/her advantages that students have to discover if he/she is a noteworthy teacher. Whoever he/she is, as a student, you had better notice what you are lacking and what you are holding in hands. After that, you may be able to communicate with the teacher what you want and want you notion is. At times, you are obsessed with something you care very much while that is not important at all for mastering a new language. A relevant advice would be put forward by a good teacher then.  I do not think there is a regular, universal rule that fits all students, so students have to uncover a feasible and efficient method to make better progress anyway.  

Happy to learn a language.