He already said his program was open to this so presumably these are non-issues. You basically then just have to find a willing program, fill in all their paperwork and orientation stuff and get licensed etc etc It is not uncommon for residents to do away rotations. For example for some specialties like forensics it is pretty common to do an away at the top programs to get a fellowship position. Some programs might want that. There are some specialt electives like UC Davis has/had a cultural psychiatry elective and commonly had away rotators. I believe Partners inHealth accepts residents from other residency programs for global health electives etc.
Of course very few (almost no) residencies provide clinical training in sexual disorders , a few more provide training in paraphilias and you will be very limited in what you can actually learn or would be able to do in month long rotation. So you may also consider approaching other clinics etc that aren't part of a residency program to see if they are interested.
TBH I dont think it would be terribly helpful for you to do a month long rotation. I would recommend doing some reading in this area, attending a course on the topic, attending conferences, finding mentors, and looking for opportunities to get more clinical exposure to this kind of thing within your residency program. I have an interest in psychosexual disorders and I think it is pretty as a psychiatrist to develop your basic skill set in this area. After all, it's totally legit for psychiatrists to talk to all their patients about sex
In fact a psychosexual history is going to pertinent in the majority of cases (okay not in the ER etc but you know what I mean). What you will find is that sexual dysfunction is extremely common in our patient population, and unless you ask about it you won't get to discover this. Add to that, many of our drugs will cause sexual dysfunction, it will be incumbent upon you to learn how to manage these troublesome adverse effects, and become au fait with prescribing PDE-5 inhibitors when appropriate.
If you let everyone know of your interests, you can become the go-to person for this sort of thing. you can select psychotherapy cases where there are clear sexual problems. You can rotate in the HIV clinic where sexual addiction is particularly common. You could develop a program in the urology clinic, in women's health, or the infertility clinic (the #1 cause of infertility is not having sex and these pts still rock up for IVF). You could set up a group for those with sexual difficulties. You want to distinguish yourself as a resource on human sexuality, relationship, sexual dysfunctions, diversity in sexuality (for example many people don't know what all the new and less new labels that have emerged to describe various facets of sexual and gender identity, or about non-traditional relationships, kink, working with LGBTQQIA populations etc etc.) When you have to gives talks or grand rounds, or choose a paper for journal club you can choose sexuality related topics. If you have to teach students or junior residents, you can teach on topics related to how to talk about sex with patients etc.
Rutger's has a program in human sexuality
Robert Wood Johnson Medical School
The European Society for Sexual Medicine offers training in this area
ESSM School of Sexual Medicine
The AASECT runs various courses and a summer institute with a different topic each year
49th Annual AASECT Conference | AASECT:: American Association of Sexuality Educators, Counselors and Therapists
NYU has a training program in human sexuality
Request Rejected
This is something you should cultivate an interest early on, develop a focus in later in residency, and realize that much of your additional training and experience will come after training as in the case for so many fields or subspecialties with psychiatry.
If you are interested in paraphilias, you may wish to do electives in forensics with sex offenders, or do a fellowship with more of an emphasis on sex offender treatment/evaluation, and/or risk assessment.