Of course there is! You just have to figure out how to do it, and what you're willing to modify in the process. I'm reading into this
that if you want to haul your bicycles on a Healey, you're probably not building a concourse contender, but rather restoring the car to drive. Therefore, yes, now is the time to incorporate the needed modifications!
If it was me...
I'd not build a single point trailer hitch, per se, but come off the rearmost crossmember almost out to the point of the spring shackles. During this phase of your restoration, it would be very easy to make a slit into which you could pass a thick (3/8" or 1/2") steel plate (maybe 3" x 4") with threaded holes tapped into it. You'd bolt your bracketry to the outside of the xmbr and into the threaded plates. From these brackets, tubular steel could be fashioned to come out from under the chassis, and up to supports the bike(s). Eight (8) bolts, and you could remove if from the car (put the bolts back into the threaded holes when not in use, to prevent corrosion) as no matter how nice you build it, without bikes on it, it will detract from the appearance of the car
Just a note about trailer-hitch mounted bike rakes:
When I wanted to put a hitch on my ///M Rdstr, so I could haul track tires to autocross events, I did a lot of searching about hitches and BMWs. By and large, nobody had any negative comments about using them to tow (relatively light utility) trailers, but there were some bad examples from when the hitches were used for bike racks! I don't know if it had to do with the single-central mount, and the wind buffeting the bikes (and no telling at what speeds these BMW_Demons were traveling...) but they were literally tearing out the sheetmetal trunkfloors of their (primarily) 3-Series sedans, coupes and cabriolets__when hauling only these seemingly lightweight bikes.
Hence my suggestion to not use a hitch-mounted style of rack, but to spread the attachment across the width of the chassis as much as possible. I would also devise some straps that you could hook to the back of the cockpit on either side, to keep the bikes "snug" and prevent them from buffeting in the wind (even thoughh we all know that Healeys are driven much slower than Bimmers
). The straps could even be kept in place with the top on, assuming it's not a BJ7 or 8.
Just some food for thought...
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but were afraid to ask: 
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Pretty Please - add it to our Events forum(s) and add to the calendar! >> 
