You might be able to build a decent AM transmitter using a 12CS6 or less so 12BE6. (the 12CS6 is more linear than the 12BE6).
http://www.wa2ise.com/radios/amxmit.html If you have enough input audio amplitude you can take away the triode audio driver.
Or solid state:

Here I used an open collector gate to chop the analog audio waveform, making AM.
Avioding hum can be troublesome, using small chokes like 100mH on the audio lines and power supply lines, as well as bypassing the rectifier diodes in the power supply (like 0.01uF) can help. The hum can come from the RF finding a stronger path thru the diodes when they are conducting 60Hz than when they are not conducting, thus making a hum buzz that looks like AM modulation be seen by the receiving radios. The chokes are to break this RF path.