So I've been in the process of applying for PhD programs over the last couple of years as I was finishing my M.Div.Honours at Providence Theological Seminary. In my researching, I discovered there are a few schools offering PhD programs which are particularly pentecostally friendly (and all of them are somewhat new programs): Assembly of God Theological Seminary (Springfield, MO), Regent University (Virginia Beach, VA), Bangor University (Wales, UK), University of Birmingham (Birmingham, UK), and the Hollenweger Center (Amsterdam, The Netherlands). All of these programs are interestingly enough distance programs...which may (in part) be due to the Pentecostal ethos of pragmatics (though this is just an assumption on my part) since they allow for continuing ministry while pursuing academics.
AGTS's program is the newest (starting 2011) and offers the more traditional American track for PhD work which involves fairly extensive course requirements accomplished twice a year (for a two week stint on-campus) prior to dissertation writing. This program is still in its infancy and hopefully will move toward more rigorous application requirements (beyond the VERY minimal language requirements in particular -- one year of Greek and Hebrew). There are four tracks available: Biblical Theology, OT Studies, NT Studies, and Systematic Theology. One of the difficulties with this program at present is also that there are simply not a great number of faculty to supervise students.
Regent University's program similarly offers coursework prior to official dissertation work. The requirements for entrance are more stringent as are the requirements for maintaining status as a student. Technically, this program is NOT a Pentecostal program...it is a "Renewal Studies" program offering tracks in Biblical Studies (OT or NT specialization), History of Global Christianity, and Christian Theology. The distinction should not be dismissed lightly. The "Renewal" nature of this program means it is more concerned with generalized understandings of the Spirit's work rather than functioning within a Pentecostally constructed framework (such as one finds in Classical Pentecostalism). This program requires on-site studies for two week stints three times a year. The faculty of Regent are top-notch Renewal/Pentecostal/Charismatic scholars in their field (Amos Yong, Estrelda Alexander, Stanley Burgess, Dale Coulter, and Vinson Synan), but sadly the OT focus (which is mine) is the weakest of all the programs for faculty qualifications.
Bangor University's program follows the British model for PhD work which is entirely research/writing as opposed to the coursework of a U.S. program. While the U.S. programs prepare a student for future studies in a broader preparation, the British program offers the self-motivated student the opportunity to jump right into the research they are intending for their final project. Bangor's program is in conjunction with Pentecostal Theological Seminary (Cleveland, TN; via John Christopher Thomas - Clarence J. Abbott Professor of Biblical Studies). This program facilitates the Pentecostal scholar to write from an explicitly Pentecostal perspective (see the works of Ken Archer, Chris Thomas and Lee Roy Martin for examples). The program functions somewhat in conjunction with the Centre for Pentecostal Theology. The student is only required to attend discussions/critiques of their current dissertation writing twice a year (for a two day stint each time) at the CPT location in Cleveland, TN (along with monthly supervisions via Skype)...and then to defend their final work onsite at Bangor (the viva).
Birmingham also (naturally) follows the British model of research/writing. They require one two-week stint onsite per year and then attendance for the viva. The Centre for Pentecostal and Charismatic Studies (at Birmingham) offers consider resources for such research and writing and offers several notable faculty (Walter Hollenweger was one of these).
The Hollenweger Center is based in Amsterdam and is a part of the Vrije Universiteit Amsterdam. There is no requirement to know or learn Dutch as a part of this program, but one must regularly visit and research onsite over the four year period intended for the dissertation (see requirements HERE). There are no specific course requirements, but any given number of seminars should be taken to aid the student in their research and studies.
If I've missed any I would love to know so that I could add them to this post. I would welcome any comments or questions about these programs as I've done the application work for all of them (plus others) [I did not apply to either Birmingham or The Hollenweger Center], but determined Bangor was the best fit for me.