I had seen a previous Instructable that relied on a single swivel caster to allow the bike trailer to turn from side to side and move up and down vertically, but then suggested a "pipe and sleeve" sort of coupler to allow trailer rotation (tilt). Although that proposed Instructable would work as suggested, it seemed to me that, with the investment in a second swivel caster mounted on a fixed frame at a 90 degree angle to the first swivel caster, you could very easily attain flexibility in all 3 planes of motion: (1) allowing horizontal turning side to side; (2) allowing the trailer tongue to move vertically up and down; and (3) allowing the trailer to "rotate" - to "tip" from side to side.
The proposed plan allows this movement in the following ways: (1) one caster wheel is trimmed flush on one side to allow it to be bolted horizontally to a point on the bicycle, and then the caster wheel frame is again reattached to the wheel, allowing the caster to turn horizontally on the bicycle mounting point; (2) the caster swivel on this first caster also allows the trailer tongue to move up and down vertically; and (3) the caster swivel on the second caster allows the trailer tongue to "rotate/tip" from side to side during travel independent of the vertical angle of the bicycle.
The parts you will need for this plan are simple:
(1) Two swivel casters of sufficient size - I used 2" swivel casters that are available at local hardware or home improvement stores for about $4 apiece.
(2) A frame to attach these casters at right angles to each other. I purchased a heavy duty right angle galvanized construction connector (i.e., Simpson), readily available from local lumber yards or construction supply stores, also for less than $4.
(3) Sufficient short bolts and locking nuts to attach the caster to this frame. I used eight 1/2" long 1/4" bolts and nylon-insert lock nuts to bolt the casters to the galvanized construction connector.
(4) Appropriate hardware to attach the coupler both to your bicycle and to the trailer frame. I fabricated an extended mount on my bicycle (see step 2) that is shown as the red square tubing in the picture illustrating this step. The trailer tongue is the black section of square tubing also shown in the same picture. I used the caster wheels as described in the following steps to attach the trailer coupler to both the mounting point on the bicycle and to the bicycle trailer.
(5) Though purely optional, I wanted to be able to quickly attach and detach the bicycle trailer from the bike; and therefore replaced one of the two caster wheel bolts with a similar diameter and length locking hitch pin that slips through the caster wheel bolt holes and the caster wheel bushing (see ring on top of this locking hitch pin inserted through the caster on the right side of the accompanying photo). This is also a hardware store item and should cost less than $4.