Dear MBA-good-but-easy:
Reading your question literally, one would conclude that you want a highly-ranked MBA program that will: admit you without verifying that you are smart; let you go to classes when you want to go to classes; and "arrange" for your employment. We are going to assume you meant "accommodate my need to continue" and not "arrange for." Nobody with the ability to write a coherent sentence could be that out of touch with reality.
That said, we still believe that your expectations are far too unrealistic. You say that you are "particular" about the school ranking, but you do not want to take the GMAT. You say that you are "particular" about the reputation of the school, but you want to pursue distance education. Alas, if only life were this easy! We hate to be the one to break it to you - sometimes you just can't have it all! Somewhere along the way, you need to manage your expectations by reaching a balance - a balance that is acceptable to you - between: your convenience, your finances, school reputation, and the hard work that may be required prior to entering the program (such as taking GMAT) and during the program. If life teaches us anything - and business education certainly does also - it teaches us that success is all about making choices: it is about making choices and sacrifices today to secure a brighter future.
While our focus for iMahal is on traditional degree education, we can make informed comments on distance learning and part-time education. Distance learning at this stage is in its embryonic stage. No one knows how far it will go and how it would eventually compete with the traditional classroom instruction, notwithstanding pronouncements from self-declared futurists or pundits. Currently, recognition and reputation of distance education does not come even close to that of traditional classroom education.
Several well-rated business schools do offer part-time programs, with very specific requirements on the duration of the program and the amount of workload a student must undertake. But there is a catch, insofar as your expectations are concerned. The reason these schools offer part-time programs is to accommodate the needs of the local high-potential talent, while the talent pursues promising and gainful employment. So if you want to pursue part-time business education, find yourself a job and apply for a part-time program in the neighborhood. You can then be "particular" about the ranking and reputation of the schools that exist in your local area. And by the way, most business schools of any meaningful reputation require the candidates to take the GMAT; and yes, it is true even for part-time education. The admission requirements and selection criteria for both full-time and part-time students are identical.
Schools in the US typically require international students to take TOEFL (Test of English as Foreign Language) to ensure that the students' level of comprehension and communication in the English language is adequate to follow the classroom instructions. Since you already live in the US, and depending on your visa status and whether you have been working in the US, you may not be required to take TOEFL.