My first thought was a 3030 also - but looking at that mounting area, it seems you could put a 5050 in there without a worry, so I don't think physical size is going to be a problem.
The two things that would be useful to know is the Vf and the current. Just checking Mouser, you can get LEDs that range from 2.95V to 6.3V and currents that range from 65mA to 400mA. The brightness ranges from 25lm to 156lm, so you could cut down on the range of interest by working out what brightness you would want - and the colour. Even then, you would have to do some homework or take a guess at the voltage/current - because you have LEDs of similar brightness that will take different voltage & current combinations. For example, around the 150 lm mark you can get one LED that runs at 3.2V 400mA and another at 6V 200mA.
If it were me, I would look at what brightness I would need, filter on the colour temperature and probably get a 6V one (or thereabouts) and a 3V one (or thereabouts). I would try the 6V one first and if that worked as well as the original, then I'd call it a win. If it was too dim, I'd then try the 3V one.
Having some real voltage and current figures would be nice, though.