As I understand it you are asking two questions:
- is it permitted to hold at an intersection of two VOR radials with nothing more than a single VOR receiver? and
- what are some tips and tricks for doing it?
Answer to question one:
As others have mentioned, it was permitted at one time (and I believe it is still permitted). I'm old enough to have received training on how to do it at a time where it was much more common to fly in GA aircraft with no DME or GPS and sometimes only a single VOR receiver. I spent over an hour researching this question for you in the AIM, Airplane Flying Handbook, Instrument Flying Handbook, and Instrument Procedures Handbook, and online generally, and was not able to find anything saying it was permitted or prohibited. I don't see any problem with it other than it adds a bit of workload to the pilot, but it can be done safely and relatively easily. If I find an definitive answer I'll update my question.
Answer to question two:
Here are some tips and tricks for flying an intersection hold with nothing but a single VOR receiver. This explanation assumes you know how to hold, including the FAA recommended hold entries.
There are two radials, hence the intersection. I'm going to refer to them here as the main radial and the cross radial. (It is possible to approach the fix on the cross radial then switch to the main radial for the hold after executing the hold entry, however, for purposes of this explanation, I'm going to assume that you are approaching the fix on the main radial (i.e. the radial on which the inbound holding course is located).
In the figure below the aircraft is on the main radial and is approaching the cross radial from the West. However, this aircraft could also be approaching from the opposite side of the fix from the East.
So, while you are on the main radial flying towards the fix, you want to spend most of your time monitoring the main radial because it is your primary course navigation, however, you also want to initially tune the cross radial well before reaching it in order to verify, and take a mental note of which side the CDI is deflected. This can be confusing to some pilots because the CDI will be either on the right or the left depending on where the station of the cross radial is located in relation the main radial. (When you fly a G1000 or HSI, the CDI rotates such that it is easy to tell when you are approaching the cross radial or have already passed it, but this is not the case in stand-alone old-school VORs). Whether the CDI of the cross radial is on the left or right also depends on if the pilot tuned in the radial or the reciprocal. For simplicity in this example, lets assume you tune in the cross radial well before reaching the intersection and the CDI is fully deflected to the left.
You then re-tune the main radial (hopefully your NAV radio has a flip-flop button), and center the CDI. You want to be as precise as possible and note the wind correction angle required and bug that heading! It's important to be precise, because you will be flying the bugged heading when you switch to the cross radial.
As you fly towards the holding fix on the main radial you will periodically switch back and forth to the cross radial until you detect the CDI is alive. At this point, you want to watch the CDI to get an idea of how fast it's moving. I like to take a note of the deflection of the CDI, lets say it is 8 degrees to the left (still haven't reached it), then take a note of the clock to determine how long it takes to fly 1 degree. Let's say that it takes 30 seconds to go from 8 degrees to 7 degrees, if so, then you know you have approximately 3.5 minutes before reaching the holding fix (7 degrees x 30 sec/deg = 210 sec or 3.5 min). You can then switch back to the main radial and continue navigating on it, until about 1 minute before you reach the intersection, at which point you would tune in the cross radial and fly your bugged heading until the cross radial is centered. At which point you would peform the appropriate hold entry.
At the moment you reach the holding fix, you will be flying the bugged heading and the cross radial will be tuned into your VOR. If you are on the main radial on the inbound heading, then it will be a direct entry and you just turn (right turn in the above figure) and fly outbound. On the outbound leg, tune the VOR to the main radial to the inbound course so that you can intercept it when you turn inbound. If you are approaching the holding fix from the opposite direction (from the East in the above figure) such that you are flying the outbound heading of the hold, then you will need to do a teardrop or parallel entry. In this case, I like to do the parallel entry because it requires less math and turning. Since you are already flying the outbound heading and are parallel to the inbound course you don't have to do anything when you reach the holding fix from this direction other than start the timer or take a note of the time and fly out for 1 minute. During this one minute of flying outbound on the parallel entry, you will tune in the main radial to the inbound course, so that when you make your greater than 180 degree turn you can intercept the inbound course.
Whether you do the direct entry or parallel entry, once you are established on the inbound course and tuned into the main radial, you will need to bug in that heading, and promptly tune the VOR to the cross radial, because you've only got a minute or so on the inbound leg to intercept the inbound course, determine the WCA, bug it, then tune the cross radial to identify reaching the holding fix.
Then repeat until you're ready to leave the hold.
This was a long explanation, but it's really not as bad as it sounds. When you are practicing this on the sim, you can try flying 2 minute legs, which gives you more time to intercept inbound, then tune the cross radial. As you get more efficient, you can shorten the legs until you get to 1 min. BTW, in actual IFR, you can ask ATC for a non-standard leg length. I imagine any airplane in this day an age with no DME or GPS that only has a single VOR is probably a very very slow airplane, and ATC can probably accomodate 2 or 3+ minute legs, just ask.