You can't constrain generic type constructors in this way (only to require a parameterless constructor), but you could take a delegate to do the construction:
public static IList ConvertTo(this IEnumerable list, Func constructionFunc)
{
return list.Select(constructionFunc).ToList();
}
And use it like this:
var IList converted = someSequence.ConvertTo(a => new T(a));