Can a Catholic be denied communion for the way they want to receive Communion?
The short answer is no.
Denying the faithful Holy Communion on the grounds solely on the grounds that the person wishes to receive the Eucharist kneeling or standing, on the tongue or in the hands is not a legitimate reason for denial.
[90.] “The faithful should receive ...
Receiving the Communion on the tongue or kneeling is never a legal reason for denying Communion.
The instruction Redemptionis Sacramentum "On certain matters to be observed or to be avoided regarding the Most Holy Eucharist" of the Congregation for Divine Worship and the Discipline of the Sacraments deals with this topic [bold by me]:
In distributing ...