It is difficult to give a short answer in general terms however here goes... The sort of in situ test that you do will depend upon the foundation type and depth and other factors such as access restraints and local ground conditions, however, you could look at cone penetrometer testing (CPT) perhaps with pore water pressure measurement (CPTU) depending on the character of the soil. Please note that the determining factor in the design may be the allowable settlement and not the bearing capacity of the foundation. Try calculating settlements first and you may find that you require a more accurate estimate of the parameters you have used in calculating settlement and that approximate values of parameters you have used in calculating bearing capoacity may be sufficient for your design.
I agree with Tom. It is a difficult question to answer for all geomaterials (clays, silts, sands, gravels, rocks tailings, etc.). The piezocone has advantage of 3 continuous measurements with depth to aid your evaluation of the ground in question. In comparison, your inconclusive results from SPT-N somewhat restricted in that only 1 number obtained. Plate bearing tests (surface) and screw-plate tests (downhole, also called "compressiometer") can give load-displacement for bearing.
I like to emphasize, with a slight rephrasing, Tom Sklucki's reply "note that the determining factor in any foundation design is the acceptable settlement". Indeed, bearing capacity is a delusion, a chimera that does not exist, and therefore, looking for a method to determine bearing capacity is like telling oneself a good joke and being surprised over not hearing oneself laughing at the punch line. The SPT gives you nothing much beyond a one-spot soil sample and, as Paul Mayne points out, there are other and up-to-date tools in the geotech's box to use in the design. No wonder that you found the SPT test inconclusive.
Despite the advances in understanding of the response of foundations to loads, the practice is still dwelling in 'geotechnically medieval times' calculating bearing capacity using various formulas including the absolute incredible one called 'THE bearing capacity formula'. To see what is wrong, take a look at my article on the subject entitled "219 Delusion of Bearing Capacity" which you can download from the web site of UniSoft Ltd. [www.UnisoftLtd.com].
The comments by Tom, Paul and Bengt are all very relevant.
However,I would like to provide some comments based on what I have gleaned from the question. The SPT being inconclusive suggests to me that you are dealing with determining the bearing capacity of a shallow foundation, rather than a deep one and that you were testing a soft to very soft clay or clayey soil. Another test that could be used is the vane shear or the pocket penetrometer. Perhaps, best of all for a shallow foundation is to use a backhoe and be able to get in intimate contact with the soil. Very often visual observations, "playing" with the soil and using experience and judgement can be quite revealing.
I am not advocating that one should not test, but rather whatever tests one does, one must have the understanding of the values obtained in relation to the compositional characteristics(fabric etc) of the intact soil as well. Sometimes this is not readily determined from the different field tests available today. Of course with constant use of a particular test method, experience is gained as well as confidence in the use of values derived.
The same could also be said for the SPT test despite its shortcomings. Indeed, no one feels cofident when the spoon moves under the static weight of the hammer and drill string or when the blow counts are hovering between 2 and 4, especially, as well, if these values occur after higher values were obtained at the previous depth of testing. Many times this low vale can also be followed by a larger value at the next depth.
These situations can be puzzling, and, if at depth, then the situation cannot be readily appreciated. Was it operator error, numbers not recorded properly, subsurface condition, etc all come into the thinking. Unfortunately, unless we know our field technolgist well, we wished we were on site. Do we then examine the geologic history of the site or try to picture that there may be something about the site and its immediate surrounds that would suggest the reasonableness of this so called erratic trend of SPT values.
Having used the SPT extensively in a particular geologic environment I have enough confidence to assess whether the values obtained can be trusted or not, or can be "teased" up or down. I would say that all test methods have their place in our practice as some, despite their advancement in development, are not very suitable in certain ground conditions. As well, the same SPT values reported for a soil in South America and one in North America for example should not be used to interpret that the behaviour of the foundations in the two jurisdictions will be the same. This is hardly ever true even if similar values are obtained in different parts of the same country, unless, perhaps, we understand the nature of the soils through their geologic setting. It is not surprising therefore that we are often unable to predict the behaviour of foundations in jurisdictions outside of our experience given only physical descriptions of soils and values derived from testing of all types.