Check out Astro.
https://www.astrotools.com/
They have handheld rivet tools, ones that are used with a drill, and pneumatic ones.
My general rule-of-thumb is to NOT use a tool at its max 'rated' capacity.
So for use on 3/16" rivets, get a tool 'rated' for use on the next size larger rivets. So that means a tool 'rated' for use on 1/4" rivets.
And if you are really set (no pun intended

) on using a handheld rivet tool on 3/16" rivets, get one with longer handles as opposed to the short compact handles. Leverage from the longer handles makes it MUCH easier to use compared to a shorter handled tool, even if the shorted handled tool is 'rated' for use with that size rivets. If your space is so constrained that you can't fit the longer handled tool into the working space, you will be getting a workout squeezing the shorter handles!
Handheld 1/4" short handled Astro #1423 rivet tool, with compound leverage:
Patented structure increases power and reduces shock Shortest long arm riveter which can operate up to 1/4" (6.4mm) stainless steel rivets Shorter hand ...
www.astrotools.com
Handheld 1/4" longer handled Astro #1426 rivet tool:
Extra long handles provide excellent leverage Includes 5 nosepieces: 1/8-inch, 5/32-inch, 3/16-inch, 7/32-inch, 1/4-inch Spent mandrels are collected in the ...
www.astrotools.com
Astro #ADR36 drill-powered rivet tool:
Item is no longer available Easily convert your cordless, pneumatic or corded drill into a power pop riveter. Includes nose pieces and works on 3/32", ...
www.astrotools.com
Astro #ADR14 drill-powered rivet tool:
Easily convert your cordless, pneumatic or corded drill into a power pop riveter Includes nose pieces for 3/32", 1/8", 5/32", 3/16", 7/3 ...
www.astrotools.com
Astro 3/16" pneumatic rivet tool:
• Includes the following nosepieces: 3/16"" (4.8mm), 5/32"" (4mm), 1/8"" (3.2mm), 3/32"" (2.4mm) • Performs well at ...
www.astrotools.com
Astro 1/4" pneumatic tool (almost twice the pulling force of the 3/16" rated pneumatic riveter):
Includes the following nosepieces: 1/4" (6.4mm), 3/16" (4.8mm), 5/32" (4mm),1/8" (3.2mm), 3/32" (2.4mm) Flip over tool to access re ...
www.astrotools.com