CG Fore/Aft Location
The further forward the main wheels are in front of the CG, the greater the propensity for ground looping.
Main wheel separation
The closer together the main wheels, the greater the propensity for ground looping.
Main wheel Toe-in and Toe-out
The following text and images come from the book "Landing Gear Design For Light Aircraft" by Ladislao Pazmany, obtained on-line via this web page on www.vincesrocket.com:
The "toe-in" and "toe-out" of a wheel is measured either in degrees or
in inches as shown in Figure 3-9.
How the "toe-in" or "toe-out" affects the directional stability and
control of an aircraft is a controversial subject. The author
consulted with a number of aeronautical engineers and landing gear
experts. The answers were mixed. Some indicated that with "toed-out"
wheels as shown in Fig 3-10, the wheel on the outside of the turn
tends to run straight and counteract the ground loop.
Other opinions were that the "toed-in" wheels result in more drag (due
to skidding) in the outside wheel than in the inside wheel, therefore
counteract the ground loop as shown in Fig 3-11.
The recommendations in some Service Manuals are that a very small
amount of "Toe-in" (0 to 1/8 inch) measured at empty weight, is
desirable. Essentially the wheels should run straight (zero toe-in)
at normal operating weight. The PL-4A (Figure 1-11) designed by the
author has 0 degree toe angle and exhibits excellent ground handling.
Any tendency to ground loop initiation is easily countered with the
rudder and steerable tail wheel. The same comments apply to tricycle
Here's a post from an on-line discussion forum for rc airplanes where the author describes a particular plane where the landing gear can be quickly removed and re-attached to convert toe-in to toe-out or vice versa. The author notes that any toe-out seems to greatly increase the difficulty of keeping the aircraft going straight when the aircraft is rolling at high speed on the main wheels with the tail in the air.
The entire thread from which the above post was taken may be of interest-- the opening question is very similar to the question here: "What design aspects affect ground handling?"
Here's another post from another related thread on the same forum where the author-- a very experienced builder and flier of rc planes-- advocates some toe-in.
Camber is a significant factor. If the bottoms of the main wheels are closer together than the tops, the wheels have positive camber. If the tops of the wheels are closer together than the bottoms (like on a Me-109 or Spitfire), the wheels have negative camber. Note that if a tailwheel aircraft has zero toe-in but positive camber when it is an a fuselage-level attitude, then the camber will automatically create toe-in when the tailwheel is on the ground. If a tailwheel aircraft has zero toe-in but negative camber when it is in a fuselage-level attitude, then the camber will automatically create toe-out when the tailwheel is on the ground. This may be part of the reason why negative camber has generally been found to contribute to an increased propensity towards ground looping, and positive camber has generally found to contribute to a decreased propensity toward ground looping. Note also that when a ground loop begins and the "leading" or outside wheel starts to get more heavily loaded than the "trailing" or inside wheel as the plane starts to tip over toward the outside wingtip, negative camber will make the "leading wheel" tend to "dig in" or experience an increase in traction, exacerbating the process, while positive camber will tend to reduce this tendency.
Tailwheel aircraft show much less propensity towards ground-looping when landing on grass or wet pavement, than when landing on dry pavement. This might seem to suggest that any tread on the tires of the main wheels--or at any circumferential grooves -- should increase an aircraft's propensity for ground looping, by increasing traction. However this related ASE answer indicates that tread or circumferential grooves don't actually increase a tire's grip on dry pavement.
It would seem that anything that increases a main wheel's "contact patch" -- which would include decreasing the tire pressure-- would increase the ground-looping tendency on dry pavement.
A high CG location increases an aircraft's tendency to tip over and drag the outside wingtip during a ground loop. Even before the wingtip touches, any tipping will load up the "leading" wheel and unload the "trailing" wheel, which will exacerbate the developing ground loop.
An aircraft with a relatively short fuselage is called "short-coupled", and will experience a greater propensity for ground-looping than an aircraft with a relatively long fuselage.1 If the mass of the aircraft is concentrated near the CG so that the moment of rotational inertia is low, the aircraft will have less tendency to ground loop than if the mass of the aircraft is distributed far from the CG.
Here is a PDF from a course on landing gear design. Note however that it doesn't go into a great deal of detail. Toe-in/out and camber are not discussed.
- This sentence naturally begs the question-- exactly how might we quantify how "short-coupled" an aircraft is? Probably not by comparing the fuselage length to the width of the landing gear tread, as this would seem to imply that increasing the distance between the main wheels is not helpful. There may be some room for further refinement of this part of this answer--