What is the best option for a gap caused by a missing tooth that is too small for an implant?

Your first option to consider may be orthodontics to create more space and move the adjacent teeth roots out if the way to make an implant restoration a possibility.  As usual,  your post gives totally inadquate information eg. which tooth, condition of adjacent teeth, bite pattern, lip line, other crowding, diemension of space available etc etc etc  and you need diagnositc information from a dental examination to evaluate your options comprehensively.  In some cases we can overcontour the adjacent teeth with bonding composite and this disguises the size of your small gap and improves the appearance for your smile (at negligable cost).  a 3mm diameter implant is the smallest implant size that would provide a reliable dental implant for a crown, but of course you need a larger gap than this to fit it in!  Don't worry, this is not a very challenging case, find yourself a good local dentist who has an interest in dental implants, works with orthodontists and is recommended by your colleagues and best of luck.