In answer to a question: As far as tips go perhaps you may want to consider the following; or use them to inspire more of your own knowing.
– If the group of you who are teaching the class have a theme or an intention, that will help to give it continuity even though there are different teachers. You also need to be clear on a general overall style (i.e.. hatha – beginner; vinyasa – flow; anusara; etc…) and level of the class.
– With the above considerations you have 20 minutes at the end of the class – an 80 minute class if there are 4 of you teaching. This would mean the students have likely done lots of warm-ups, sun-salutes, standing poses, and hopefully by then at least one peak pose. If the person teaching before you takes them to the peak pose depending on what it is, you could play off of that opening (hips, shoulders, back extensions, etc….) and add another dimension or move right into counter-poses and their cooling down sequence. There are many options to include here depending of course, on what they have done previously.
– You mentioned wanting to do pranayama with them and being perhaps a little nervous about that. One of the simplest and effective ways to teach and do is to incorporate it with movement such as is the case when doing mudra (vinyasa). I would suggest sama vriti – equal breathing, with some deep long holds in forward bends. You could have them end with a small sitting practice of sama vriti (pranayama) to seal it in.Every aspect of a yoga class is important in a different way, however I believe that the beginning and the end have the most lasting impact on students as these elements set the tone and leave them with their lasting impressions. Desikachar is a wonderful teacher and inspiration and many of his vinyasa variations would be a great way to wind down a class. Depending on the style of class, your focus/feeling or bahva and what the person before you is teaching you may want to remain seated for your segment or start standing and then move to the floor and provide a relaxing, cooling portion for the class. Generally I finish with students enjoying some gentle floor work such as a variation of Upavistha Konasana incorporating side bending flowing up and down with the breath. Or other hip openers such as Pigeon, Janu A or Baddha Konasana. Forward folds are also great for closing, however whatever you do will depend greatly on the overall focus of the class.
In terms of Pranayama I find Nadi Shodana or alternate nostril breathing is very calming and a nice way to close before final relaxation. During Savasana there are many beautiful poems or readings you could choose from such as Rumi or excerpts from books like ‘Meditations From the Mat’.