The tire is not the issue with holding air, unless you have tubeless rims/tires but that is very unlikely. Your innertube holds the air. You can have a slow leak in that. I have a tube on one of our bikes that needs to be aired up a bout every 3-4 days. Most times I only need to air every 7-14 days. Some are much more sensitive to their pressure and will air before every ride.
In any case, a new tube should fix the air holding problem. Check at your LBS for what size tires your rims can take. What size are they now that you think they are too thin? Wider tires will not roll as easily but will give a better shock effect. Although that seems a little unnecessary as I think your bike has suspension.