The F2H-2B was externally similar to the F2H-2, but had some local strengthening of the wings so that the aircraft could carry a 1650-lb Mk 7 or a 3230 lb Mk 8 nuclear bomb on a big pylon underneath the port stub wing. The flaps on that side had a small cutout for clearance of the store. An in-flight refueling probe installation was subsequently developed that could be installed in place of the upper right 20mm cannon.
The -7 was a very large weapon which required increasing the pressure in the main landing gear strut to provide even minimal ground clearance. This is my guess at the pylon shape and bomb location; note that the shock strut has not yet been extended to provide a modicum of ground clearance. (Read on for a description of this system on the F2H-3/4, which may also have applied to the F2H-2B.) I've subsequently discovered (see below) that the tail cone had to be rotated clockwise (viewed from the rear) to provide clearance with the J34.
This is a picture of VC-4 F2H-2Bs aboard Lake Champlain sometime between June and November 1953. Note the flat-bottomed inboard stores pylon which was probably used for the Mk 8.
The F2H-2B was reportedly manufactured alongside the "stock" F2H-2 and -2Ps on the McDonnell production line. 27 were listed in an appendix to the F2H maintenance manual (Also see comment below).
For some reason, the location of both the refueling probe and the bomb mount were switched on the F2H-3/4, with the bomb now being carried on the right side and the refueling probe installed on the left side of the nose.
For pictures of the probe installation, see http://tailhooktopics.blogspot.com/2012/03/f2h-34-inflight-refueling-probe.html
Whereas the F2H-2B had the cutout only in the left side flaps, the F2H-3/4 had the cutout in both flaps.
This is a preliminary sketch that I made once upon a time.
Thanks to the Gerald Balzer collection via Mark Nankivil, I now have better pictures of the Mk 7 and Mk 8 being carried by the F2H-3/4. (The Mk 7 shown has different fins that shown above and appears to be have a blunter nose.)
Note that all the shock struts are fully extended to provide a modicum of ground clearance although a video of a launch suggests that only the main gear struts were over pressurized to load the store; the nose gear strut was subsequently extended as usual for the catapult launch. This picture also shows the tail cone on the Mk 7 being rotated counterclockwise (looking forward), in order to clear the jet tailpipe; it's not clear on the video, but it appears that this wasn't absolutely necessary.
The struts were only partially deflated automatically when the landing gear was retracted "to permit a landing with stores still aboard" (presumably not on a carrier), which was why there were two separate tanks. To remove the remainder of the extra fluid from the struts for normal strut action, the pilot had to actuate a switch on the left console after he had lowered the landing gear.
This strut extension capability was provided by a kit, suggesting that it was only added to aircraft designated for the mission. I have read that the F2H-2B strut extension was provided with "sleeves" added over the exposed piston. These reportedly dropped away after lift off. However, I don't have any documentation on that yet so I can't say that's myth or fact. It may have been an early kludge to provide the capability before the strut extension kit was developed. I also don't know whether just the bomb-side strut was extended on the F2H-2B or both sides. My guess would be both.
The Mk 8 picture was even more welcome. It was mounted on a slightly different pylon and also required the shock strut extension to provide clearance for the tail fin group. Note that this aircraft is equipped with the inflight refueling probe replacing one of the 20mm cannons and the fairing on the belly associated with this modification.
The shape shown below is the BOAR, a Mk 7 with a rocket attached for better separation from the instant sunshine it created.) Note again that the main landing gear shock strut is fully extended to provide what clearance there is but the nose strut has not yet been extended.